The Seasons and the Earth's Orbit - Milankovitch Cycles
"We would not expect the 21,000-year cycle to be very important climatologically because the Earth's orbit is almost circular - the distance to the Sun at perihelion is only about 3% less than its distance at aphelion. That is, whether perihelion occurs in January or July, it seems unlikely that our seasons would be much affected. At least, that is the case now; but the eccentricity of the Earth's orbit (how elliptical it is) also changes over very long periods of time, from almost zero (circular orbit) to about three times its current value. The eccentricity of the orbit varies periodically with a time scale of about 100,000 years. So, it would be reasonable to suppose that if the 21,000-year perihelion shift cycle were to have any effect on climate at all, it would only be during the more widely-spaced epochs when the orbital eccentricity was relatively large. That is, climatologically, the 100,000-year cycle of eccentricity should modulate the 21,000-year cycle of perihelion.
"In fact, Mars has an orbit much more eccentric than the Earth's, and its perihelion cycle (which has a period of 51,000 years) does apparently have a significant effect on climate and prevailing wind
direction there."
http://aa.usno.navy.mil/faq/docs/seasons_orbit.html

This discusses the effect of Mars' perihelion cycle, where perihelion occurs in the year, on its climate change. However, how extreme can Mars' orbital eccentricity get? At the current level, it results in
40% greater solar illumination at perihelion than at aphelion. Note also this results in average global temperature of about 0°C:

Hubble finds Mars' climate harsher than thought,
http://rossby.metr.ou.edu/~spark/AMON/v1_n3/news/MARS.html
"Mars has two distinct climates that usually are associated with periods when it is nearest to the sun and when it is farthest. That happens every Martian year, which is equal to two Earth years.
"When Mars is nearest to the sun, it gets 40% more sunlight than when it is farther away. The extra sunlight warms the average surface temperature by 80 degrees, to about zero, and stirs up continental-scale dust storms on the surface. The dust is swept high
into the atmosphere, turning the sky pink and blanketing the planet."

This also raises the average pressure over the planet above 6.1 mbars due to the seasonal melting of the southern polar ice cap.

A recent report suggested changes in Mars' obliquity resulted in large amounts of surface ice at middle latitudes within the last 100,000 years:

New Images Reveal Martian Ice Age, Signs of Water
"A new global map of Mars has revealed a host of valleys carved from otherwise smooth areas that might be signs of the Red Planet's most recent ice age. The features also bolster the case for a vast reservoir of water ice just below the surface."
http://www.space.com/scienceastronomy/solarsystem/mars_hummocks_010726.html

However, according to the "The Seasons and the Earth's Orbit - Milankovitch Cycles" page, Earth's climate cycles, I presume measured by glacial cycles, correlate more strongly with the timing of the eccentricity cycle:

"The 21,000-year perihelion cycle and the 41,000-year obliquity cycle do in fact appear to be present in the climatological record. But the dominant climate cycle that is seen has a period of about 100,000 years. Although this coincides with the period of change in the
eccentricity of the Earth's orbit, the theory outlined above does not predict that we should see this period directly - the effect of eccentricity should appear only as a modulation of the 21,000-year perihelion cycle. The mechanism by which the Earth's orbital
eccentricity could affect the climate in such a direct and important way is not known, although recent evidence (published in 2000) indicates that atmospheric carbon dioxide may play a leading role in
amplifying the orbital effect. However, some researchers still have doubts about the association between the 100,000-year climate cycle and orbital variations. Thus, many questions remain about long-term climate variations and their relationship, if any, to astronomical causes."

Then perhaps the change in eccentricity would have a greater effect on Mars climate than the change in obliquity. Is it known how close Mars' gets to the Sun at its most extreme orbital eccentricity?
The argument that the eccentricity cycle should not directly effect the climate cycle seems strange to me, at least as presented on this page. Certainly I understand that change in eccentricity should have
an effect on how the perihelion cycle effects climate, but I don't understand why this means change in eccentricity doesn't itself effect climate. I'm assuming that at high eccentricity the planet would reach
a closer distance to the Sun at perihelion than at moderate eccentricities.

Also, interesting on this page is the fact that the closeness of when perihelion occurs to when the start of Winter occurs, or Summer in the other hemisphere, has an effect on climate:

"The Earth reaches perihelion - the point in its orbit closest to the Sun - in early January, only about two weeks after the December solstice. Thus winter begins in the northern hemisphere at about the time that the Earth is nearest the Sun. Is this important? Is there a
reason why the times of solstice and perihelion are so close? It turns out that the proximity of the two dates is a coincidence of the particular century we live in. The date of perihelion does not remain fixed, but, over very long periods of time, slowly regresses (moves
later) within the year. There is some evidence that this long-term change in the date of perihelion influences the Earth's climate."

Currently Mars' perhelion is offset some months from the southern Summer, occuring in southern Spring. Then it is quite likely that when perihelion and southern Summer coincide there would be even greater
melting of the southern polar ice cap with an even greater increase in global atmospheric pressure.
What would be the effect on the climate of Mars when these three cycles were at their most favorable for temperatures on Mars, when perihelion coincided with southern summer, obliquity reached its
maximum, and orbital eccentricity was at its highest value? Could it allow open water seas on the Martian surface?

A Scientific American article that discussed climate change on Mars is available online:

Global Climatic Change on Mars,
by Jeffrey S. Kargel and Robert G. Strom
"Today a frozen world,
Mars at one time may have had
more temperate conditions,
with flowing rivers, thawing seas,
melting glaciers and, perhaps,
abundant life."
Scientific American, November, 1996,
http://www.sciam.com/1196issue/1196kargel.html

Bob Clark