So how cold is it outside, how milky is this fluid, and how long have you let the tractor run. Before I invested a $ in parts or ripping anything apart I would drain the fluid from the bottom of the rear end case, both sides and toss it. Go to Tractor Supply or whatever you have out there and get a $30 pail for universal Hydro/Transmission fluid and fill that sucker up. If the cold thick fluid couldn't get through the screen to the pump nothing is going to do a thing, if its milky and its cold out it will thicken just enough to not pass through. Clean the screen with some kerosene to make sure nothing is clogging it, kerosene should flow through it easily.
Kerosene and $30 worth of fluid and you will know if you have a strainer/fluid issue or you need to rip apart and look for whats broken.