I wanted to consider the possibility that the "spiders" were due to liquid flow because of the dendritic features seen. However, I neglected to consider the possibility that they may be due to liquid CO2 beneath the ice cover rather than liquid water.
The Gamma Ray Spectrometer on Mars Odyssey 2001 may be able to make the distinction or find the relative proportions of water and CO2 beneath the surface:

Mars Exploration Program
2001 Mars Odyssey Orbiter
"2.1.2 Gamma Ray Spectrometer (GRS)
"The experimental objective of the GRS is to determine the elemental composition of the surface of Mars by full-planet mapping of elemental abundance with an accuracy of 10% or better and a spatial resolution of about 300 km by remote gamma ray spectrometry, and full planet mapping of the hydrogen (with depth of water inferred) and CO2 abundances by remote neutron spectrometry."
p. 2-2
http://mars.jpl.nasa.gov/odyssey/pip/2001MarsOdyssey-PIP2.pdf

However, the GRS will only be able to see about a meter below the surface, so in the case of the spiders the determination will have to be made during southern summer when the CO2 ice cover over the spiders dissipates. If a significant fraction of the flow is due to water then you would expect it be within a meter of the surface, though without the cover probably as ice. However, a possibility with the subsurface CO2 component this close to the surface is that it might also sublimate along with the CO2 cover as the temperature rises, giving the mistaken impression that the flow is due entirely to water.
Another problem is the large resolution scale of the GRS at 300 km. If the spiders are distributed over a wide area this might still work. Also the sensitivity of the GRS is not very great at 10%. If the percentage of water is only 1% it probably couldn't detect it.
Interestingly, the GRS also has the capability to detect subsurface carbonates, though again at the 300 km resolution scale. The sensitivity will probably also be 10% or above. This might address the speculation that the carbonates on Mars are hidden beneath the dust cover on Mars. The expected sensitivity of the GRS of the various elemental abundances is discussed in section 3.2.3 Spatial Resolution and Sensitivities in the report.
The THEMIS spectrometer of course will have much better resolution and sensitivity for carbonates but it won't be able to detect them subsurface.

Bob Clark