First, check the outfitter's rating at www.OutfittersRating.com. There is a question specific to the condition and safety of camp and field equipment in every survey sent out on the outfitter's behalf. Be sure to review that rating carefully, as proper, safe equipment in a critical element in both the success and enjoyment of any hunt.
When you're talking with the outfitter prior to booking a hunt, get very specific in the questions you ask about equipment. Ask him for brand and model of treestands he uses, for example. Ask if he replaces them on a set cycle. How old are the oldest ones in use? You'll be able to judge as much by the way the outfitter answers the question as the answers themselves. If he hems and haws like he doesn't really know, it's a warning sign you should heed.
Ask the outfitter specifically about what gear you are responsible to bring and what he or she will provide. Safety harnesses should be a requirement of any outfitter utilizing treestands in his operation, but are they provided, or is that something hunters are required to bring.
Once all your questions are answered to your satisfaction, make certain the details of the gear to be provided and the gear which you are responsible to bring is covered specifically in the booking contract you sign with the outfitter. If it's not, handwrite it in, sign it, date it, and require that the outfitter does the same.
Dealing with outfitters highly rated in the OutfittersRating.com system, chances are great you won't ever be disappointed in the condition or safety of the equipment provided for your use. However, it never hurts to nail down the details. For example, if you left an agreement that simply said, "Outfitter to provide horses for transportation," you could be in for a bad surprise. Will each hunter have a horse? Can/will the horses be used for hauling out game? Is there a wrangler in camp to care for the horses? Are the horses for transportation from the trailhead to camp only, or will they be used for actual hunting as well?
These details will likely impact your decision to make the hunt in the first place, and will definitely influence how you plan for the hunt. So the best advice when it comes to assuring the quality and safety of the outfitter's equipment -- Ask LOTS of questions and make sure you get your answers in writing. Remember, trust by verify!