First I'd check the chain laws in your state.
In Oregon if the trailer has brakes
and chains are required they're also required on the trailer. 4 Wheel drive and AWD are exempt from the chain laws except when towing.
I'm figuring on buying chains for my Scamp
. I'll also watch the weather and try to go into the mountains when I know the roads will be clear and chains won't be required. The thinking is to have the chains if needed but attempt to avoid situations where they would be needed.