As already stated the worst problem is usually the viz reduction. however, you may be already aware that one of the very few helicopters that are truly all weather is the Super Puma, heated blades, special intakes etc et al.
However, a real danger to a helicopter is rain / clear ice which has been known to build up extremely rapidly, is highly "sticky", is very heavy and will change the aerofoil shape of the inner third of your rotor blades as well as goo up your external control runs and unheated transparencies, aerials etc. Thankfully it is rare!
We used to suffer really badly whilst ground taxying in slush. If it was allowed to freeze on the wheels it became:
CHOCK-ICE!