I, along with many other folks who live in wintry mountain environments, share your situation. Keeping a semblance of running form through the winter while shifting priorities to ski touring, skimo racing and Nordic skiing requires a bit of creativity but in the end I think it offers advantages. The muscular endurance gains which you’ll get on skis will carryover well to your ultra, and i think offering the body a few months’ respite from a high volume of high-impact such as running can be a good buffer against overuse injuries.
In terms of connecting the dots with TSS for skiing vs. running, the easiest method is to stick to comparable heart rate values, using your designated AeT as an upper bound for most sessions designed to be aerobic. Use a consistent fudge factor for your vertical gain (we typically use 10 TSS per 1000 feet) and use hrTSS for your ski touring/skimo workouts.
While you’re correct that the muscular load is somewhat different for skiing, in that there’s no impact, you’re carrying more weight, etc., they’re not so dissimilar as to not provide a decent representation of your ongoing fitness through CTL measure.
I would recommend maintaining a base volume of running throughout the winter season – maybe ~15 miles per week – in order to keep the impact-resistance in the muscles so you can merge quickly into the spring season when skiing starts to wind down. One easy way to do this is to incorporate short (3-4 mile) recovery runs several times each week in the afternoon/evening after your ski days.
Hope that helps,