Rain or shine, I would never drive on tires with 2/32nds of an inch of tread.
Here are just some of the problems:
- Your emergency stopping distance is greatly increased.
- Your risk of out-of-control hydroplaning is greatly increased.
- You are much more susceptible to road hazards going through the tread.
- Your traction is reduced on all surfaces.*
- Your ability to maintain control to avoid an obstacle is reduced.
- Because of the above bullet points, the odds of getting in an accident are significantly increased.
- In many places, you are subject to getting a ticket and getting fined. In some places, your drivers license can be suspended or revoked. Also, in some places, your vehicle can be impounded for being unsafe to operate. (This is especially true if your physical appearance does not match that of the law enforcement officer.)
- If you get in an accident, your insurance company may try to not cover you, because you did not properly maintain your vehicle. To make matters worse, sometimes insurance companies will take "measurements" of your tires and claim they have even less tread. (A friend recently got in an accident, and the insurance company's "measurements" were 2/32nds of an inch less than the actual tread depth... lucky for my friend, I know how to measure tire tread depth and had access to their vehicle at the junkyard.)
Overall, in your case, it would be better to rent a vehicle or buy your second choice in tires.
I will disagree with the answer that advises just to "drive defensively". Although driving defensively is always a good idea, you can never account for all the idiots on the road with you (or the fact that all of us are likely one of those many idiots at one time or another... I know... "not me!").
Note that it's easy to check tire depth. Every tire shop will do it for free, or you can buy a tool to check it yourself. If you buy the tool, make sure to learn how to properly use it. There is also the "penny trick", but the tool is so inexpensive and much more accurate.
The best advice is to check your tires frequently for:
- Tread depth
- Sidewall wear
- Sidewall cracking
- Embedded items (rocks/nails/screws/glass)
- Uneven wear
- Damaged tire valves
- Missing valve caps
- Proper inflation
At the same time, you can check your wheels for:
- Missing balancing weights
- Loose balancing weights
- Missing lug nuts
- Loose lug nuts
- Cracks or other damage
During your routine inspections, you will then notice the tires are getting down to 4/32nds of an inch of tread (or more tread, if the conditions warrant it). At that time, replace them promptly**. If you do this, you, and everyone else on the road with you, will be safer.
* Note that the TireRack article linked to by Moab (but not written by him, so it's not his fault!) is exceptionally misleading when it states: "A practical example of this is the racing slicks used on stock cars and open-wheel racers that provide traction at over 200 mph." Those racing slicks use different compounds and completely different ratios than your tires... In my opinion, TireRack's example is nonsensical, thoroughly misleading, and potentially dangerous.
** When you replace your tires, check the dates on each tire (embossed on the sidewalls) to make sure none of them are old stock. Also make sure the model number and size on each tire matches all the other ones.