I'd wait for the ice to clear, first of all. Unless I have proper winter shoes with snow pads and borium, which is sadly not done in Britain, I won't go out in conditions like that.
If my horse wants to be strong on the trail, she has work. Hard. Shoulder-in, half-pass, turns on the haunches, lots of little circles, reinback, anything I can think of. The other trick is when you come back to the barn, go out again in a different direction. She normally doesn't play that game but sometimes has her moments, like on Monday when I had her out after a winter of very little hacking and she'd forgotten the rules. She absolutely perfect until looked at her watch, realised it was tea time, and then wanted to hurry back to the barn. We circled, shoulder in'ed, the lot, until she agreed to behave and then I stayed on the road PAST the barn for a couple hundred yards, before turning around.
The thing to not do is ride a prancy, pulling horse back to the stable and then get off and finish your ride. This will only encourage the behaviour.