I am aware that it is a really bad idea to march with a wood piccolo, but is it possible (if the right precautions are taken) to march with a wooden one the whole season leaving it undamaged? Please tell me what I could do to prevent cracking and whatever other damage could be caused.

You need to keep the temperature and humidity swings to a minimum. IOW: No cold weather and not wet weather. In a marching band situation it`s impossible as you suggest unless you live in a warm & dryer climate like Southern Calif..
Best thing to do is find a cheap used Plastic one and save your wood Picc for concert time.

~Bilbo