Hi, I've been playing horn for 7 years and I'm looking to learn a new brass instrument. I'd like to start playing euphonium, but I don't know how possible it would be or how detrimental it would be to my embouchure.
Any input is appreciated.

I doubled on a sousaphone and trombone for marching band in high school. As long as you're not playing it "full time" compared to your french horn (i.e. more than twice a week for me, personally, now that I don't practice as often), I think it's perfectly alright to do. In fact, you may learn something new about your embouchure and breath support that wasn't apparent when playing french horn.

Having a great sound on horn while being able to maintain at least a passable sound on other brass instruments is something I like to strive for. It shows you (a) built a good embouchure for horn and (b) have great breath support.

On that last note, pay special attention to your breath support! If you drop support, your embouchure will definitely suffer as you try to squeeze sound out. This is a no-compromise zone. Bad breath support = bad playing = you hurting your embouchure.