OP, get some fenders if you don't have them. Fenders expanded my riding time (and enthusiasm on wet days) because the bike is kept cleaner so I don't think about it - and they keep the road grime and snail guts off me. I did a group ride this morning - last half hour we got showers, but it was reasonably warm and wound-up about as damp as I would be on a humid day. I carry a couple plastic bags for my phone, etc.
Wider tires with a file tread work pretty well on wet roads - still need to be careful.
Pouring rain or cold rain is a no-go.