Yes, your plant is damaged. I had that happen to an aloe that I left on a windowsill overnight, when the outdoor temperature unexpectedly dropped down to the mid 20s. I had closed the drapery over the plant, and the cold air collected between it and the window glass.
Your plant will survive if you provide good care for it through the winter. The key is whether the crown and central leaves are undamaged. If they are, then all will be well; if they are also damaged, the plant is unlikely to regrow.
Here is some information I found through Google:
Frost-damaged Aloe Vera
I have a beautiful LARGE Aloe Vera plant that I have had as a house plant for over a year now. I was living in Mobile, Alabama, where I could leave the plant on the porch. Now I live in Atlana, Georgia, and I had the plant on the patio, until we had some freezing temperatures one night. I realized I had left the plant out and brought it in the next morning. The plant is wilting. It has "seeped" some fluids, some of the partial leaves are still firm while others are completely withed, the most center leaf is still bright green and standing tall.
Now my question is what do I do to attempt to revive the plant? Do I cut the wilted leaves at the base, leave them aloneÃ‚Â ?? Please if you have any advice, guide me.
Your aloe has certainly been damaged by the frost, but it sounds as though the roots and the growing crown have survived. That's good news! Bring the plant inside until the cold weather is over to avoid additional damage.
Trim back the damaged leaves. You can take them all the way back to the soil if they're severely damaged, or just cut back to healthy material if they're only damaged at the tip. Dry the cuts as much as you can. Succulents are prone to rot in moist, damaged tissue.
Water the plant lightly, and in a few days, give it a very light feeding with a balanced fertilizer. It should look better in a few weeks.