Yes, rim brakes on muddy going are hopeless, alwsy getting clogged up like that. That front wheel you listed should be ok, narrow rims can take surprisingly large section tyres without trouble.
Roller brakes are a little slow acting and seem weak after other types, but on the rear wheel those are good attributes, lessening the chances of a lock-up. They are popular on utility bikes which are mostly used at lower speeds. You probably don't need the cooling disc at the speeds and short braking periods you'll be experiencing off-road, so you could leave that off to make for even easier cleaning in that area.