I do this all the time for the outside patio 120VAC things we are using. I also run an extension cord from the 20AMP Pedestal inside the trailer to run my two oil-filled portable heaters. Being a POPUP trailer it is easy for me to run extension cords into the trailer thru the window flaps. The Pedestal 20AMP Service has its own circuit breaker and will not pull power from the 30AMP Shore Power Connection side... It also makes good sense to me to use the power from the pedestal instead of consuming your Propane for heat if that works for you...
Typical Camp Ground Pedestal
I only use the propane furnace here as the last resort for heat as it is too much heat for my OFF-ROAD POPUP and the furnace blower consumes too much 12VDC power from my batteries.
One should be careful however that is using the bigger trailers as the Propane Furnace provides the heat source for the under belly tanks and some inside plumbing to keep from freezing...
Plan your 120VAC usage and do what is best for you. It is there to use...
Roy Ken