I have several folders in the Move To dropdown menu, and I'd like to keep the labels but hide some of them. Advice?
You can't. That menu holds all of your labels. The only way to remove a label from that list is to remove the label altogether.
If you're having trouble with finding your more important labels amongst a long list, I suggest changing your label name to have some sort of non-numeric character in the front. I do that with a handful of my labels to make sure they're at the top of the list.
So instead of
Now my "Joe" label is at the top rather than halfway down the list.
You can change the name of a label to make sure that it sorts at the top of the list, a number or and underscore works great.
You can't hide a label from the pull down list but you can make other changes:
When looking at the list of labels under "Move to" or "Labels" You can used the manage labels command to hide a label from the sidebar list