A few simple questions

Air cooled means that the cylinder head and engine is cooled by air flowing around the engine, just like a lawnmower.
Your foreman 500 does not have a radiator. It does have 2 oil coolers that look similar to a small radiator and apparently some are relocating them to keep mud and crud getting all over them. Hope this helps.

it is smart to put your radiator on you front rack if you ride in alot of mud, because once your radiator is full your bike will over heat like crazy. you can do it to any bike that has a radiator, it dont matter what brand or anything. a air cooled motor has "fins" on the head of the motor so the air will cool it. the other kind is called liquid cooled motor, this kind does not have the "fins" on it. that is the purpose of radiator on the liquid cooled bikes.
you could just drain your oil to see if it is milky and if it was not milky you could put the old filter back in be i do not recomend it. there is also a dip stick you can use to see if there is water in your motor, this would be alot easyer than draining the oil out. hope this helps.
-Aaron

Now, the 07 Foreman's only have one oil cooler. Just in case you are looking for them.

thanks for the info guys. yeah i see the one oil cooler, mine doesnt have any mud in it.... i really dont see me putting my 4wheeler in mud that deep to get it stopped up... water maybe!

Yeah I have put mine in muddy water up to the headlights and haven't seen anything in mine either. One thing to watch for, even just with water, is grass and other debris getting in there. Something else I heard on here, by the serious mud riders, is to look at the back of the oil coolers too. The front will look fine, but the back will still have a solid wall of mess. Just some more info for you to watch for. Hope it helps.

I have read about this so called ONE oil cooler on the 07's. I think they still have TWO. You won't have any overheating problems, don't even worry about relocating. Overheating is more of a problem with liquid cooled machines.

I put a big oil cooler on mine because the weather this year is suppose to be weather breaking heat waves. You can check out mine in the form (how much power is in your foreman what mods do you have?) I have a lot of pics. My bike runs around 280 degrees. If you have any questions just ask.