We treat all our horses with a carrot slice when they come to us. Once slice. Any other food requires the correct completion of one or more behaviors. They also know they have to wait their turn or they will be run off from the group with no treat. Nor "horsing around" when "mom or dad" are out there. But unless the other horse was trained like this I surely would not do any food rewarding.
We have a stallion and his daughter who are very food protective and food aggressive and both bit me once. The stallion bit me when I was removing a knot from his mane when he was eating. I chased him for about 10 minutes throwing acorns at him and from that point on he has to back away from his food before he gets it and he has to back away while he's eating if asked and we've had him for about 9 years, showed him and just fun ridden him with no problems but he is NEVER allowed to remotely threaten. The daughter was very bossy because her mom is THE herd alpha and the daughter thought the rest of the mares were afraid of her so she got a bit of an attitude and when I brought her grain she thought I stayed a bit too long and bit me on the hand. I chased her around and threw rocks at her and the funniest part was when the other mares would just step aside so I'd have a good shot at her butt. It was like "It's about time you dealt with that young'n - she is seriously full of herself" Well she never tried that again.
But there is always that risk of another horse trying to run off the one you're working with if it's close enough. I won't even go into an area with a strange horse if I'm carrying a bucket even if it's empty because they will go after you to get that grain.
I have used grain for clicker and it works fine and ours are trained well enough so we can use it on a trail ride with another of our horses and the second horse won't go after it but that's because they know their own rider will reward them.
One advantage of using a food reward and carrying a few carrot slices is if you should for some reason fall off the horse, the horse is much less likely to leave you and run off. We've had several occasions where a saddle slipped or a horse did a quick turn that caused one of use to lose balance and just slide off and in all cases the horse stay either right with us or stopped very soon and waited for us.
But NEVER give food unless the horse performs a designated action or you WILL get a mugger and that is so dangerous. A trainer friend told me about one she got in for training that was so bad she had to smack the horse upside the head with a bucket to get her to back off and we bought one who also had been treated extensively and I had to kick him in the shins with steel toed boots to get him to back off and give me my space. Nothing else would get that horse out of my lap. He looked so hurt but he did back up and THEN he got his treat so he perked up and figured it out just fine and now is always respectful. He was really a difficult one. We had to use two flapping jackets and two longe whips to get him to even move out in a round pen. He just wanted to hang with us and not move. Again once he did what was asked and then got his treat he was fine from then on. Really smart horse but BAD habits.
So absolutely be careful. You can do two horse at once IF you have two people, plenty of room and the horses aren't aggressive but you'd better know your horse and stay away from fences when you clicker train.