1. Who is making the offers? Your average hairdresser is an employee, they have no interest in spending their day managing offers online, and it doesn't offer them the experience they're looking to gain. This means the salon will need to hire another person that can make offers to individuals online, or the owner themselves will need to take on this extra work. This can't be anyone, they need to be familiar with different hairstyles, their difficulty, and rates.
2. How much time does it take to acquire a customer by making offers? What happens if the customer asks questions online? How much is a price for X? Oh, that's too much, what about if I do Y? Would you be willing to lower your offer from $25 to $20? Then, they disappear. I have a feeling they'd waste a lot of time making offers, while seeing little return. The cost is simply too little for the time spent communication with individuals.
3. How does this compare to hiring someone to stand in front of the store waving a sign? As someone else said, haircuts are impulse purchases for a lot of people, so if you have someone standing on the street, telling people walking by that haircuts are 10% off today only, would they bring in more customers then someone online making competing offers? With the sign, at least the person is already standing next to your salon, so they'll convert to customers better than someone online.
4. Who is this for? Most people have a regular hairdresser that they have a relationship with, so I'd think they're unlikely to change. When I relocate to a new city, I just check Google maps for barbershops or salons, and the majority have reviews. I pick one closest, with positive reviews, that focuses on men's hair. That's it.
The idea of businesses making offers to customers isn't a bad one, but I think you need to rethink the niche, hairstyling isn't a business where I could see this working.
Edit: I had to step out for a bit. To expand though, what if you applied this to a different industry, like cars? I could say I'm looking for a 4 door car, max budget X dollars, and local dealers could submit cars they have available with their best offers. Car dealers are pretty competitive, so I think they would be more willing to put forth effort to chase customers than a hairstylist. Also, if you make a sale, you could earn a thousand in commission, instead of $2. I'm not saying it'll work, that was just a general suggestion for why you might want to look towards other markets.