"But!...It makes me wonder...could there have been an close analogy to the present-day climate in Iceland in a locarge but localized area on Mars billions of years ago?

As You know, Iceland would have a climate and ground conditions comparable to northern Greenland, or even Antarctica, were it not for two things:
(1) The Gulf Stream.

(2) Tremendous and widespread geothermal activity not far below
Iceland's surface. "

The Antarctic is much colder than Greenland. Most of Greenland is north of Iceland. Iceland latitude is comparable to Norway or Alaska.

"The Gulf Stream keeps average yearly temperatures in Iceland around 40 degrees, which is much milder than might be expected at this latitude on the edge of the Arctic Circle. The weather, however, is highly variable and anyone traveling to Iceland on a brief vacation, summer or winter, should be philosophical about seeing the sun. Strong, gusty winds can be depended upon."

Volcanically active regions will only warm area in a very local sense- hot springs many allow vegetation [due to warmth] in a similar way that river in desert supports vegatation.

In addition the large glacier regions of Greenland will have cooling affect on other regions in Greenland.

Another aspect is that air is transferring warm ocean temperature. Without a dense enough atmosphere on Mars, if you had a large body water it wouldn't necessary be effective in warming land areas near it. A very warm large body of water heated by geothermic could make the area around it colder by covering it with bright white ice/snow.

Suppose you had nuclear reactor heating a small lake on Mars. Suppose the same lake on Earth would kept at say 70 F. What happens on Mars. Would it cycle from being frozen to a certain depth, then briefly melting and then rapidly cooling and freezing over again?