yes generally it's 'ok'.
the trailer has some of the same features as household wiring.
but with a few extra features (12 volt) and with many limitations.
almost every 1500
watt appliance (and all space heaters) comes with a warning...
NOT 2 use an extension cord (even those labeled heavy duty)
there are several reasons for that warning beyond corporate CYA.
so using an extension cord plugged in outside and snaking into the trailer is not a good idea.
there are many threads and websites that explain basic wiring and electrical limitations (rv specific)
there are even books specially on rv wiring/power/12v and ac/dc issues.
when connected to shore power,
the trailer is essentially a giant extension cord with breakers.
so IF you over load any one outlet or any one breaker bad things may happen.
it's important to know about the 'shore power' source...
-is it 15/20 or 30 amp?
-is the voltage proper?
-what is the capacity of the wiring and junctions and so on...?
how much (if any) does the voltage drop as amps in use goes up?
get out a multimeter or buy a display gizmo and check the shore outlet.
then check the trailer outlets.
find the breaker box and look at the 4-6 breakers (there should be 1 30 amp and a couple of 15/20s and a couple of 20s)
determine WHAT is connected to each breaker and where the appliance outlets are on those breakers.
while many of us do use space heaters safely, we've also had the experience of OVERLOADing a circuit.
simple things like flipping on the water heater (if it has an electric option),
or running the fridge on AC, while trying the microwave, or CHARGING the batteries...
in combination these things will overload.
and IF the shore outlet is only 15 amp with standard household wiring,
using a 1500
watt space heater may be an issue.
((is that smoke i smell....