This may be a dumb question, but isn't this more of a "movement detection counter" rather than a "people counter"? Nothing sets apart an animal vs a human triggering this, right? I was imagining a camera with CV processing the images or something.
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.