I would'nt recommend running 18" tyres on 10" rims on the trail, but 20" tyres on 10" rims shouldn't be an issue.
My Aluminium douglas 9" rims on my quad get bends/dents in them all the time but my standard 10" rims on my Tecate have yet to have any problems.
I would have no problems recommending running standard 10" tecate rims with 20" tyres for trail riding.