Tyvek is not a substitute for insulation in any way at all. You can use fiberglas or rockwool batts, or rigid foam insulation board, whichever you prefer. Mice have a harder time burrowing into the latter but they *can* if they are really really dedicated. Make sure that whatever you use, it is panelled over on the inside so the chickens can't peck at it.
Insulation is DEFINITELY worth it in cold winter areas, b/c it allows you to maintain a decent temperature (like 20 F or so) while still having as much ventilation as possible. And you NEED good ventilation in the wintertime, just as much or more as in summer.
Have fun,
Pat