I'm watching The Empire Strikes Back and that is the question that I had when watching the first few scenes. That's a pretty crappy planet. Luke and Han are on a recon mission during which there is a blizzard and some sort of huge snow monster nearly kills Luke. He escapes only to wander through the blizzard, which has gotten worse, and barely survives thanks to Han.
That's a dangerous place. Not to mention that the rebel forces seem pretty small and the planet doesn't seem to have many natural resources they can draw from. So why shouldn't the empire just sit back and wait them out?
Vader senses Hoth is where they are hiding. I can understand if this was the last of the entire rebel alliance and the empire wanted to wipe them out in one last stroke. But I doubt that is the case given the sizable coalition the rebels have in Return of the Jedi. Regardless, Vader wants to invade Hoth because Luke is there. Upon learning that the droid has exploded on Hoth, he says that he is "certain Skywalker is there". To me that suggests his primary concern is finding Luke, not so much crushing the rebellion.
That sparks another question. Why is Vader so concerned about Luke? Its only later in the movie that Vader talks to the Emperor and is told that Skywalker is the son of Anakin and therefore must be destroyed. Vader then says that turning him to the dark side would be a good move and thus makes it his expressed goal to find him.
During that conversation with the Emperor is Vader hiding his emotions and intentions? I'm not sure because the first movie and everything up to this point in Empire doesn't say how they know Luke is a Skywalker (unless I'm not remembering something). The only contact Vader has with Luke in the first movie is right before Luke blows up the Death Star. And Vader's only comment is that "the Force is strong with this one". Does Vader later conclude from this encounter that this person is a Skywalker? Or do him and the Emperor talk about things in between the first and second movies and come to that conclusion? It can't be the latter because of the conversation I mentioned they have later in Empire. And after just watching that conversation, Vader says that he has felt the "great disturbance" in the Force that led the Emperor to conclude that the rebel who blew up the Death Star is Skywalker.
So I guess my theory is that Vader knows that Luke is his son from that encounter at the end of the first movie (also he knows who Leah is without the Emperor telling him, so he seems to be able to just feel it). And then when they attack Hoth in Empire he is doing so because he wants to find Luke and have the conversation they have in Cloud City at the end of Empire. I think Vader doesn't go all mushy on Luke because he is either still conflicted between those feelings and those towards the Emperor and the Jedi or he can't reveal his true emotions because the Emperor would find out and kill him and Luke. I'd go with the former because of how hesitant he is at the end of Jedi to save Luke and kill the Emperor. Only after the Emperor is gone can Vader embrace his feelings about Luke. But I think his actions regarding Hoth show those feelings where there all along, just buried really deep down.