Need advice for Rochester, MN

You could Google "rochester, mn. dog parks, open year round"

You're smart to research ahead of time.

We had a day to kill last fall in Elkhart, IN when our RV was in for repairs. We were shocked to learn that their dog parks are "member only" and that it was going to cost us $30 to go to any of their municipal dog parks. Guess what were empty all day? Yes, the municipal dog parks.

We found a dog friendly bar instead and had a grand old time.

Not suggesting you find a bar for the day. Good luck to you and your husband.

If you are looking to while away a couple of hours, try Quarry Hill Nature Center on the east side of town. Just a few minutes from any of the Mayo facilities. Of course it is winter, and it all depends on when it last snowed, but should be a good spot to do a short stroll (or longer, depending on weather). Dogs have to be leashed. Check out the old sandstone "caves" (actually old food storage for the old State Hospital).
You may want to give a call ahead about whether they have cleared some of the paved walking trails if it has just recently snowed.

https://qhnc.org/

Thanks for great ideas. I never thought of the dog park. I know there is one south of downtown that we have been to before. I'll check out the Nature Center, too. Sounds interesting. I really appreciate you taking the time to help me out. Thanks again. Tracy