Putting wider wheels on a hybrid bike
Frame clearance can be a problem, especially if the mud is sticky and the tire too close - it can clog up quite badly if you go too wide. If you have V brakes, these can also, however my experience has been worst case is new brake pads. 

29" Mountain bike tires are 700C. (As Always - http://sheldonbrown.com/tire-sizing.html has the answer), so you now have a wide range of tires to choose from. The web page also has a great chart for tire width vs Rim Width compatibility. With a bit of luck you will not need new rims, just tires. 

If in doubt, take the bike to the guys at the LBS and have a chat with them. They will put you right on local conditions and will hopefully know the route you are riding and give good suggestions.