Thanks for all the suggestions. The car cranked back up yesterday and rran fine for a while. Im still not sure on whats causing it but we are running reccomended oil in them and they have plenty of gas in them. Temp is starting to get down to around 30F and tops out around 50F during the day. Its only this one engine that is giving us a problem the others once they warm up do just fine for the day.
What kind of engine are we working with here?
If its a Honda or clone engine like your other dirty air filter thread, (you already tried replacing the air filter on this one right?) try pulling the fuel line off at the carb and see if your getting a good strong flow of fuel. If its just barely dripping, unscrew the sediment bowl/fuel filter built into your petcock. Maybe its just full of dirt and restricting the flow.
This would totally explain why it might run alright for only a short time after its been sitting for a few hours and finally had a chance to completely fill the float bowl.
Another possibility here is that you've got dirt plugging your carbs needle and seat valve or its main jet. On Honda's, you'd want to remove the carb and unscrew the bolt at the bottom-center of your float bowl to remove it. You'll then see how the needle and seat/float assembly comes apart. After removing this spray some carb cleaner in through the carbs fuel inlet, and also from the other direction through the small fuel orifice you'll find in the seat valve to thoroughly clean the passage. Clean off the needle and seat and reassemble.
With your float bowl off, you'll notice the carb has a long tube that protrudes down nearly to the bottom inside of your float bowl. Your main jet is inside there. The jet unscrews with a fairly wide straight blade screwdriver but you can usually leave it in to clean it. Just find a small diameter needle or something small that you can push through the Main jets small orifice a few times to clear any debris, and then insert your carb cleaners straw tightly up against the jets orifice and spray the cleaner through it. (just hold it so the carb cleaner cant blow back into your eyes while doing this, it really hurts)
I've got a feeling your fighting 1 or maybe a combination of a couple of these problems with that engine but you might as well try them all. Sometimes its also a good idea to clean out any dirt or debris that tends to build up in the gas tank so similar problems dont soon reoccur...
One last thing you could confirm (while your air cleaner is removed) is to make sure your carbs choke butterfly is fully opening when the choke levers in the open position.
All this talk about rejeting for cold weather is just to get max performance in race kart engines and wouldn't apply to your problem here. I think its just a coincidence it started acting up now and you'd be having this same problem if the weather was warm.