I have first year hollyhocks in pots in zone 3. They are very healthy plants. I plan on overwintering them inside in a cool place. Do I cut them back or do I just leave them and slightly water them until putting them back out next spring?

Don't leave them outside in pots. The 'rule of thumb' for plants in pots is they need to be hardy 2 zones below yours. The roots wouldn't survive the winter. But they do go dormant and will need water. I would wait until they die down naturally then cut them off and stick them someplace where you will remember to water them. Keep them below 40°F (4°C) to instigate next summer's flowers. I hope your pots are big.