You could address this with the woman but the underlying issues with DH would still be there. You shouldn't need to address this with the woman, it is with your husband the issue lies. He should be setting boundaries with her. If she then breaks those and your DH is feeling uncomfortable and she still won't back off, then I would say it is acceptable to speak to her yourself.
TBH I do understand U26 point about finding a new hobby and perhaps there is nothing else to it, however a lot of what you have said OP goes beyond an enthusiasm into unacceptable behaviour. Stopping foreplay to text this woman back? Texting at 11pm at night? Texting for over 20 minutes and ignoring you? Not acceptable. You're not being a jealous idiot at all; those are very big red flags. Considering some of the other things you are now saying, about changes in appearance, I would be very worried.
I would seriously consider moving the horse. I know you said it wasn't an option as the horse is settled but honestly, what is more important, the comfort of this horse or your marriage?
Moving the horse is a good start but it might not fix everything, as perhaps there is some underlying cause to DHs behaviour. Do you spend a lot of time together or have shared interests outside of DC/home life? Once you move the horse, could you get more involved with it with your DH?
Right now I would be sitting DH down and telling him very strongly that his behaviour is jeopardising our marriage. I would set limits to the contact that is acceptable, try to talk through what it is that might be causing this behaviour (are you spending enough time together?) and try to rectify it (for example, as I said above, doing more things together and getting involved with the horses more yourself).
If he didn't agree or broke his promises then I would be kicking him out asap - not necessarily LTB, but just to show that I take this really seriously.