A hot sauce is not "hot" in terms of temperature, but in pungency (or spiciness)!
In other words, yes, your hot sauce can freeze.
The question is, is it good for the sauce?
The answer again is yes. You can freeze your hot sauce, whether it is homemade or bought.
Do consider the following points, however.
- If the sauce contains chunks of tomato, onion, capsicum (bell pepper), etc, they will get mushy.
- Depending on the preservatives contained in the sauce (if any) and if it was heat-processed, the shelf life of your sauce once you've thawed it may vary. Watch for signs of moldiness or bad odour but generally a hot sauce will last a good 2-3 months.
- If you put a glass bottle of hot sauce in the freezer (especially one that is full), it may break. When a liquid freezes, it expands, which means that you run the risk of having a messy freezer and a bad time cleaning it up. Consider not filling up your bottle to the top and leaving some airspace, or putting the bottle in a ziplock bag, just in case it explodes.