Sam,
Yes you can provide hot water for a radiant flooring with a geothermal heat pump. You can buy a unit that is a "water to water" type that uses ground heat/water to then heat water that is stored in an insulated tank. That stored hot water is then used in the radiant floor system for heat.
Here is one such water to water unit (I have no financial link to this or any GTHP retailer).
Buy Goodman Heat Pump | Geothermal Heat Pumps | Goodman Air Conditioner
The above is a 4 ton unit that will provide 48,000 BTU (40 kBTU) per hour. I don't know your total envelope insulation values, so I can't tell you if this will provide you enough heat when it is -15 F and windy.
Even though you can "reverse" the GTHP cycle and provide cold water to the floors, as in summer for cooling, your humid summer environment does not allow this. You regularly have dew points in the high 60 to mid 70s F. The reason is that you will literally have wet floors when the cold floor is below the dewpoint. To get much cooling, you need the floor about 45-50 F and that is WAY below the summer dewpoint.
Example. Put a glass of cold water on your kitchen table in the summer. That water is about 40 F or so. Note the condensation on the outside of the water glass? That is what your floors will be like. So radiant "cold" does not work for your location.
A small (compared to heating need) tonnage ac unit is called for. It could also be a GTHP.
WaterFurnace, a physically close to you manufacturer of GTHPs, makes a unit that not only provides chilled or hot air, but also radiant water for a loop. Problem: $$$$$ about $10k+
WaterFurnace Residential Product Line : Synergy3D
Personally, I would start with a water to air GTHP from Ingrams such as this:
4 Ton 2 Stage GeoCool Geothermal Heat Pump
The above is a 4 ton (48kBTU) unit that will certainly provide enough cool in summer and likely 60-80% (?) of your winter heating need.
Many people in your area use open loop systems where water from their domestic water well is used. The output water from the GTHP goes into a pond or such. Least expensive, and where lots of ground water is available and a high water table (such as you have), it is a very rational solution.
But again, we are just guessing at the tonnage size needed. You need a assessment (manual J or utility) or a load test for your home such as I described above. I can tell you with winters like you have at least 3 tons for heating and perhaps as much as double (triple?) that, depending on the above results. Your summer cooling load is low, so any system that provides sufficient heat at -15F winter will cool off a house when it is 95F summer.
No point is spending more for a heating/cooling system that you need.
Or read the manifesto and build your own . . . .
Steve