First time on the trails..

I got a 4yo TB mare about 3 weeks ago. At the place where I board there aren't really trails that go through the woods, but there is a BIG hay field with lots of hills that we ride around.
Last week I took her out with just 1 other horse and she was pretty good- a little spooky, but otherwise behaved. Yesterday I took her out with 3 other horses and made her walk in the back. She felt like she wanted to race them the whole time. She bucked a little and trotted side ways, but then she calmed down a little once she realized that wasn't going to get her closer to the front.
I want to take her out in the field because the hills are great exersize, but I can't always have someone come with me. And eventually she needs to be able to do cross country by herself.
I was wondering if I should just go out by myself and handle what she throws at me, or if I should keep going out with a group untill she calms down a little.

Personally I think its what you think you and your horse are capable of. I know for me one of my horses in no where near ready to go out by himself. He just isn't mentally there yet doesn't listen to my cues when he is nervous or to excited.

As for my other horse I can take him out all day with minor spooks where he just freezes snorts settles then continues on like nothing happened.

If you think the horse can go out by themself with you go for it, just do as much as you can to limit any problems. Like if she is really hot or hotter then normal lunge her before going out, wear a helmet or some protective gear, carry your phone on you and not on your horse, MAKE SURE YOU TELL SOMEONE WHERE YOU ARE GOING AND STICK TO THAT!!

Have a goal set in mind and do not try to do more then that goal.
Realistic goals are anything from riding for 30 minutes to 2 hours etc, or riding 5 miles total etc. just don't push it. And remember if your horse spooks at something like a creek or jumping a small tree in the way be prepared to work through it and not let them get away with it. You want the first ride out alone to be positive and you want to make sure you work through any problems so that there will be less issues next time. So make sure you are not on a time limit

Ok. It takes like 30 minutes to walk around this field and its just grass and hills- that's it. My main goal I guess would be to just make it around with out bucking or her trying to run. I will definatley do about an hours ride before the trail though because it can be really hard to calm her down mentally.

just make sure before you go anywhere your horse has good brakes, and responds to all your cues. If they do not then they are not ready. Also just a tip make sure your horse knows how to bend so when/if she gets hot on the trail you can make her bend to get her to refocus on you.

What I have found works for my young guy, is doing a normal "training" session first and then go out for a ride. I find that for him it gets his brain settled into working and gets rid of excess energy. He has really come to love going out with or without horses now because its his relax time.
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She could actually do better on her own. She may have been competing.

My opinion is that to get a horse used to trails by themselves, you take them on trails by themselves. As long as you can handle your horse without getting hurt, take her out alone. It will take more than one or two times out to calm her(horse time), but she will get it.