(youtube video to accompany this article)
While we are always impacting our horse's behavior and they are always influencing ours, it's important to have time with your horse outside of "formal" training sessions. With R+ focused training, a lot of tension can build up surrounding your presence because it often predicts the start of a training session, which happens to involve a lot of good stuff for the horse. They WANT to train and are actively looking to initiate that training session with you.
They are looking for the predictable cues that indicate to them that a training session is about to begin. A common "predictor" for many horses is just the presence and arrival of their human at the barn, or near the pasture fence. If every time you arrive at the barn or approach the pasture fence you start a training session, they may be confused and even become very frustrated when one day you arrive and you just want to "hang out" with them. Sure, hanging out with you can be reinforcing in a social way, but it's not nearly as exciting as when they get to offer behaviors and get clicked for it.
Lifestyle, diet, health, and mental activity play a HUGE roll in this too.
A horse that has been fasting for the last couple hours or more will be even MORE eager to start a training session that involves food.
A horse that lives in a mental dead zone (dull pasture, no enrichment, no companions, etc) will ALSO be very very eager to mentally and physically engage in an activity with you. "Hanging out" is probably the last thing on their mind to be honest, they've been doing that all day. (unlike you, who were probably thinking you could use some downtime after a stressful day of running about and taking care of stuff)
And a horse that has health problems like ulcers, that make food a source of relief for them, making it challenging for them to just "hanging out" when usually your arrival predicts food availability... and that's what they need to feel better.
So we need to be careful just going into the pasture and hanging out without offering our horses something else to do, if this has been their history with us (our arrival = training), and we also need to be looking to come up with a new reliable cue for the horse to know it's time to offer behaviors and vice versa. Simultaneously we need to be looking for ways to make the rest of their lives more enriching, healthy, and natural so that our arrival isn't a form of relief to them.
With time and intentional actions we absolutely CAN (and SHOULD) spend time with our horses outside of formal training where the horse is totally at ease with our presence, and it won't have to be so "organized". But for those of us who find ourselves with horses that never tire of looking for opportunities to start training, we have to be patient and careful as to not cause frustration for our horses or dangerous situations for ourselves.
And for those of you who are freshly starting off with R+, take this as a helpful tip as you go down this new path. Try not to hyper focus on the training sessions, and spend time with your horse where you have no expectations of them so that you don't accidentally teach your horse to expect to start training every time they see you.
Create a different "start of session" cue that you can be predictable with. And try starting your sessions when your horse is engaged elsewhere, to encourage them to go about their day until the predictable cue is given.
Also, end your sessions respectfully with your horse. Don't just pack up the food pouch, target, and clickers and say "goodbye I'll see you next time, enjoy your dry lot". Leave them with an enrichment activity, food that's of distracting value, and with a nice big jackpot to make your "parting" just as positive as your arrival.
Trust me, you will thank me for this later. ;)