One of the things that still amazes me after over a decade riding around here, is how quickly it comes good after rain. Even biblical type stuff, all it takes is a couple of days of wind and a bit of sun and the trails are mostly dry again. Still, there are times when the weekend doesn't coincide with one of these dry spells, and you have made the trip anyway. Your bike is ready, your buddies are here with you, and your motel room is getting smaller by the minute. You GOT to go riding.
You can, and not get in too much of a mess or damage the trails too much. You just have to choose your trails wisely. I will assume you have a map and can follow it. Your big loop if you are pretty good riders should start from the carpark and go up Nursery and Katore Roads to Gunna Gotta. Unless it is pissing down this trail is cool. It drains well. Follow it through to A Trail and Tickler, then go up Direct Rd, Lobotomy, to the start of Billy T. Ride that, turn left to Loop Rd/Split Enz. Head down that to Pondy New, follow the road to StirFry and Sweet & Sour. Take Dragons Tail or Be Rude Not To, then ride the road back to your car.
If you are not up for such a big ride, or your group is less skilled, ride out of the carpark onto Tahi Trail, follow on to Creek, then on to Nursery Road. Take the road to Ball & Chain, follow that through to Yellow Brick Road, turn left after that to go up to Pondy New, then follow the directions above back to the carpark.
Other trails that hold up well in the wet are Genesis, Challenge, Turkish/Soakhole, Hot X Buns, RockDrop, Rosebank.
Trails to avoid are the Dipper, or up on the hill any of Tuhoto Ariki, Huckleberry Hound/Little Red Riding Huck, and Corners. Unless you LIKE mud and carnage, in which these are the ones to head for.