You can get them out if you just twiddle your finger clockwise on their bodies. I used to do that but then I learned that twisting them any way made them regurgitate and therefore more likely to pass on any diseases they were carrying.
I also used to mash any I took off the dogs between my fingernails to make sure they were good and dead.
I now have Lyme's disease. Most likely from having been bitten by ticks myself, but I can't help thinking about all those crushed ticks and the inevitable cuts on my hands.
So however you deal with them, be careful.
Personally I'd get some proper, effective tick treatment for your horse - any chemicals are unlikely to be as nasty as the diseases ticks can carry