I'd be a lot more cautious about her being a four year old than her being a mare. Although she was given to you, so its not like you went out looking.
I've owned two mares and two geldings, and leased a fair few other geldings. One of the mares was my favourite horse ever, I raised her from a yearling and had a great bond with her as she grew up (I had to sell her as a five year old though). Even then though, she would have her moody moments and if you got angry at her for something on one of her days she would refuse to talk to you, and just turn her head away even if you had carrot. She was the best horse ever.
My other mare that I had after her was a real b*#$* and disliked me.
If you get a long with your horse and haven't had any trouble then I wouldn't be overly worried. Its not like the entire horse changes overnight, she just might be a little more irritable, and they are rarely dangerous when in season. Geldings are generally more even tempered, but thats not always good - you can get a gelding who is always crazy!
Besides that though, be careful with your four year old. She is not at a stage of education where she can teach you - you have to teach her. If she does something that scares you then make sure you take care of it right away, because if you shrink back she's going to keep doing it. Confidence is extremely important with you horses - honestly if I had to choose between someone with lots of knowledge and no confidence or a bit of knowledge and confidence I would consider going with latter with young horses.
So if you are scared, don't show it, pretend not to be. Horses like strong people.
Good luck though - welcome to the forum - there are lots of people here who are more than happy to help you. And congrats on your new horse