Considering the temperatures this winter, as long as the roof didn't leak, it's probably been preserved pretty well in the deep freeze. Mold should be the least of your worries in upstate NY in winter.

If the toilets and other water traps in the house are dry, then sewer or septic gases have been pouring into the house and it's going to reek!
Usually, you'd pour anti-freeze into the traps if you're turning the heat off.

You should be able to air that out by opening windows though, and as soon as you get there run water into every drain to block them off from sewer gas again.

my surprise - in a house without heat all winter - basement floor heaved

My main concern would be that the house temperature would get lower than freezing and that the pipes would burst. Even if the utilities are shut off, the water pipes could contain enough water to cause damage, even if the taps were all opened. You may not have water spilling out if the water is shut off, but when it is turned back on you will find out if you are going to have flooding.