I've generally never had an issue storing small gas engine tools outside over the winter as long as they're kept dry.

Bought a decent pressure washer this year and was wondering if it will be ok assuming it's drained. Alternatively I can move it to the dirt cellar but it's a pain.

Thoughts?

I keep my pressure washer in an unheated shed every winter. Completely drain the water, Stabil in the gas and I like to put a little vaseline on any of the rubber O-rings at the disconnects so they don't dry and crack.
Never had any trouble.

Water freezing in the lines biggest issue, drain thoroughly maybe even flush with antifreeze. I keep forgetting to flush and have it freeze and break things several times...:(

Treat your fuel with a stabilizer.