I'd look seriously at the TRAFx counters I referred to in my other comment. They'll do exactly what you want, they're used to count backcountry skiers by quite a few organizations, they work great in winter down to at least -40C.

There are some non-trivial design problems that need to be overcome in outdoor environments. The ultrasonic sensor may not be a good choice for winter counting, frost buildup on the sensor surface will likely greatly affect performance, plus it's a bit of a power hog.

Don't forget that battery capacity/max current can be greatly affected by cold temperatures as well.