There is an interesting podcast that I listen to - We Martians. Last Nov they had an episode that touches heavily on this. The episode is here: http://www.wemartians.com/home/015 and it goes into far more detail than I can, but here's a brief summary:
The SHARAD (SHAllow RADar) instrument on the Mars Reconnaissance Orbiter used ground penetrating radar on the area of Mars known as Utopia Planitia. The radar results, while not definitive, strongly suggest "a mixture of ice, air, and dust" in the area. "SHARAD detection and characterization of subsurface water ice deposits in Utopia Planitia, Mars".
This information was presented in context with info from the Phoenix lander. The lander was equipped with a robot arm which dug in the soil. This article describes it further: "The Dirt on Mars Lander Soil Findings"
Using its robotic arm, Phoenix dug into the Martian surface to see if
it could reach the ice below.
In one trench, dubbed "Dodo-Goldilocks," the lander exposed what
mission scientists described as "bright material" about 4 to 5
centimeters below the surface (a similar patch was seen below the
lander itself, likely exposed by the spacecraft's landing thrusters).
Over the next two months, the team watched as Phoenix's cameras showed
that the material was sublimating away, which would be expected of
water ice exposed to the Martian atmosphere.
The tendency of soil samples scooped up by the lander to clump
together made it difficult to get the samples into Phoenix's onboard
instruments, but after several attempts, a sample was coaxed in and
the lander's detectors confirmed that there was indeed water ice
hiding under the regolith. The confirmation was originally announced
on July 31.
Interestingly, the ice seems to occur at different depths under the
surface depending on the terrain. The plains where Phoenix landed
feature polygonal mounds surrounded by troughs that result from the
seasonal expansion and contraction of the ice underneath the surface,
which creates cracks and crevices.
And from this related article: "Water Ice on Mars Confirmed"
NASA's Phoenix Mars Lander has confirmed the existence of water ice on
Mission scientists celebrated the news after a sample of the ice was
finally delivered to one of the lander's instruments.
later in the article:
"I'm very happy to announce that we've gotten an ice sample," said the
University of Arizona's William Boynton, co-investigator for Phoenix's
Thermal and Evolved-Gas Analyzer (TEGA), which heats up samples and
analyzes the vapors they give off to determine their composition.
"We have water," Boynton added. "We've seen evidence for this water
ice before in observations by the Mars Odyssey orbiter and in
disappearing chunks observed by Phoenix last month, but this is the
first time Martian water has been touched and tasted."
The news that ice had fallen into TEGA came on Thursday morning,
surprising scientists who had run into problems delivering a sample of
the icy dirt because of its unexpected stickiness.
Opinion: I'm not sure any of this is 100% definitive proof of there being sufficient mineable water for producing Methalox, but it does strongly suggest that at least in this part of the planet there is significant water just below the surface.
Future missions will study this issue as well.
The Trace Gas Orbiter may provide more information once it's fully online - it has the ability to detect neutrons4 from sub-surface hydrogen (which may or may not be water) and trace H2O in the atmosphere5.
The ExoMars rover and NASA's Rover 2020 will both carry instruments that can contribute to this.
ExoMars Rover, specifically, will be carrying the WISDOM ground-penetrating radar which should be able to see subsurface ice6, and it's core drill is equipped with Ma-MISS, an infrared spectrometer that should be able to determine the presence of water or ice in the drill site7.
NASA's Rover 2020 will also carry the RIMFAX ground penetrating radar8, as well as other instruments for chemical analysis - I am not sure if any of them are specifically aimed at ice detection. Of related interest is the MOXIE experiment, which will attempt to extract O2 from the martian atmosphere.9