I know @2DogsFarm IRL and I can tell you from experience she smells good! I think there are two factors here: your barn and you. When my kid attended a school that had a stable, the students who came from the riding program to the classroom “smelled like the barn.” I noticed it too when I visited the school (boarding school) and we attended her classes after a visit to the barn.
However, at our home where we have a stable, this is not the case. One can (and has) go to the barn, feed, turn out, and immediately go to work (although I generally wore coveralls if feeding in my work clothes) with only a change of foot wear.
I was (retired now after 40 years) a teacher --and trust me --those high school students will TELL you if you smell of anything --young people have a very acute sense of smell. So I feel confident that a feeding visit to my barn left no odor. I never went to school after working horses or working with horses. Just the quick feed in the AM.
The difference is I don’t keep my horses inside. The school where the kiddo attended kept 130 stabled horses (beautiful box stalls, cleaned twice daily) --despite the ventilation, fans, open doors, that place smelled --of horses --true --but smelled. I have three horses (five stalls) --no windows, but the East-West ends of my stable open completely and capture a breeze --that and the fact that the horses are in maybe an hour a day (feeding and hanging about while I work with one of them outside) means very little smell --the exception is the week I have hay delivered for the year --the smell of fresh cut and baled alfalfa is heavenly --and predominant.
I organize my day so that all “grubby work” is done at once --usually in the AM --horses, garden, cleaning trailers, etc --then mid-day I shower and dress for “town” --even if I am not going. Husband occasionally sees me at my filthiest (after using the chainsaw or weed whip) but usually, by the time he’s home (he still works), I am clean, neat, and tidy. Call me the 1950s housewife, but it gives me joy to hear a compliment from him even after 45 years of marriage.
I guess the short answer is --arrange to wash up after barn chores or change your horses stabling habits (I know everyone can’t do a 24/7 turnout like I do, but it works well for me.)