You should absolutely do it. When I was 19, a very good friend of mine (2nd mom type) had a stroke and went to live in a nursing home. I used to sneak my cat (her favorite) in to visit her. This was before they had official programs for animal visits, and I got busted by the director of the home. She was a great and open minded director and decided that I should keep bringing the cat to visit as long as I would be open to visiting other patients as well. I used special shampoo to keep dander down, and carried her vaccine documentation and brought Nikka every Monday to the home. It is amazing the affect she had on people, especially stroke victims. I later started bringing my fox terrier as well. My cat and dog loved the attention, the patients showed tons of progress with their physical therapy and some of my best memories were made. I continued to take them even after Katie (my friend) died and helped get more people involved. This was 20 years ago and when I visited that same home a couple of years ago I found they had a huge program for bringing in all different types of animals and had birds and fish that permanately live at the home. My parents raise mini horses and take quite a few to different hospitals and places like Ronald McDonald houses.
Be careful though, it is very addicting and a blast to do. I don't know who was more excited for Monday to roll around, the patients or me.