It's from the first line of the Umapyoi Densetsu lyrics. Roughly speaking, it's a unique 'constructed' portmanteau word similar to writing, say, "horseypals".
There's not a definitive meaning for the word yet (unlike, say Umapyoi), but fans will use it in a way similar to some of the more jargon/euphemistic use of Umapyoi (see sense 3. and 4. of Umapyoi as noted in post #4508118). Basically it means to get 'friendly" (i.e. "be pals") with a given umamusume. This "friendly" may be platonic, romantic, or straight-up *ahem* hanky-panky stuff.
TL:DR: It means to be "horsepals" with somebody. Or "horsebuddy". It can mean what it means (on the surface), or something deeper behind it under the cover of euphemism... if you know what I am saying.
Some continuum along the "Horsefriends → Horsepals → Horsebuddy → Horselovers → Horsefuckbuddy" scale, depending on context.
So window shopping is your job now!?I-I'll have to Umadacchi you...That was for work...Don't you get distracted! Eyes on me!You went out with that other Trainer, Kiryuin, didn't you!Trainer, you are my Trainer, you got that!If you don't...
