Will heat strips thaw my PLASTIC pipes from my washer?

I think your heat tape would work fine here, your washer hoses are some kind of rubber, and I don't see that melting at the low temperatures heat tape puts out. Another thing you could do is simply unscrew these hoses, and bring them inside to thaw for a little while. More concerning, though, is the washing machine solenoid valves (the plastic part the hoses screws onto) and the washing machine pump. Those parts always have water in them, too (and freeze, and break). I'm not sure you can adequately protect a washing machine that sits in a freezing environment, although if you covered enough parts up with heat tape it might be worth a try. Replacement parts tend to be pretty expensive, though. I wouldn't do it, personally.