What I think you're really concerned about is the amount of amp draw created by the heater. A 1500 watt (pretty much the max for a space heater) would draw around 13.5 amps. That's close to 1/2 your 30 amp service. But you'll probably not be running it at full power all the time. Here's an example of a space heater that has multiple power levels and is either thermostat or timer controlled.
https://www.amazon.com/Aireplus-Radi...ag=googhydr-20
Wiring to your 110v outlets in the trailer should be either 15 or 20 amp so you'd be well within the safety limits.
Concerns about freezing the plumbing need to be addressed as well. Cold air under the trailer can cause the interior plumbing to freeze. Your city water supply needs to be protected as well. A little more information about your planned environment would help with suggested options in this area.