Would this effect occur if an ice planet was put into orbit or trajectory?
Welcome to Stack Exchange! I'm a little confused about your question, but I'll answer it the best to my ability. 

First of all, I would like to state that such scenario is near impossible because getting the planet there would be extremely difficult.

Second of all, when the ice is being "blown", it would have to be perfectly aligned with the Earth not just in its position in orbit, but also in its angle of orbit.

Third of all, the ice would have to travel probably hundreds of kilometres, meaning that it would either 1) not make it by getting in orbit around the Sun / melting or 2) get lost in space. 

The heat of the Sun can barely move things at all - I assume you're sort of thinking of a Light Sail, but that's light, and ice would be too heavy anyway.

Getting the ice off of there would also be challenging because its connected to the planet, and can't just be "lifted" by heat. That's why the Earth's surface doesn't float / scrape away by the Sun's heat.

Overall, I do not think it would be possible. 

Hope that helps!