I don't know a whole lot about electric blankets and the safety risk there Larry. A power inverter is a relatively safe device, provided it is fused proeprly. That means both the inverter itself and the connection path that you choose to use to the battery.

I have a couple of inverters ( one 750 watts, one 300 watts ) that I use here in the home for electrical emergencies( with marine batteries as the power source ) and to play my keyboards outside without having to string a huge power cable to the spot I want to play in. They work without a hitch.

Grounding is another issue ( important when using sensitive electronic devices ), but in your application, it should work fine, provided the elctric blanket itself is safe and the inverter has the capacity ( watts )to run it,

AJ