I generally avoid swamps during the winter. The snow makes it so you can't see the "swirling" before the tentacle shows up as a little mound. It makes them much harder to avoid.

Fun tip. Chester can tank a tentacle. If you manage to get Chester to stand right next to a tentacle, the tentacle will attack him. Then you can swoop in and kill the tentacle w/o taking damage. If you try this more than once in a row, Chester will die, forcing you to wait a day for him to re-spawn. If he was empty, though, there's no need to wait, since it's the dropped inventory you'll be waiting to collect. I'm not sure the cool-down period between when you could do this again w/o killing Chester.

Also, Bee mines will kill a tentacle, no problem. They are a rather expensive way to kill tentacles, though.