I am going to come off a house panel going 250 feet to a pedestal for my motorhome. What is the smallest wire I can be by with. I will be running in the motorhome the air conditioner, refrigerator and hot water heater.

Thers'a a handy calculator for this here:
Voltage Drop Calculator

For 120 volt service, 50 amps, 250 feet you need a 1/0 gauge conductor. But 50 amps seems like a lot - drop it to 25 amps and 4 AWG would work.