How can I avoid mud from splashing onto my back without a rear wheel fender?
Use a seatpost-mounted rear mudguard, like the SKS X-tra Dry:



For the front, you can also use a downtube mudguard like the SKS X-board:



These are convenient for bikes which don't have proper fender mounts/fenders would interfere with clearance/fenders need to be easily removed or not [Most mountain bikes fit this thing]. They don't protect the drivetrain from crud thrown up from the wheels so they aren't great for improving drivetrain life on a road bike, but this is not a concern for your riding. 

The other option is to wear clothes you don't mind getting dirty.