How do mares act when in heat?

To a degree, it depends on the mare. With some mares, you don't even notice. With others...

Signs of being in heat include:

Lifting the tail and winking and showing the vulva. This "invitation" behavior is most often aimed at stallions, but if there is no stallion on the premises, mares will invite geldings, other mares or even people!

Sensitivity on the back and sides. Yes, mares in heat can get cramps and sometimes need a dose of a mild painkiller.

Acting distracted and being unable to focus when being ridden. Mares in heat will tend to call more to other horses, will become stressed more when on their own, and may have difficulty focusing. I've even known mares who are clearly trying so hard to concentrate, but they just can't.

Urinating frequently and producing only small amounts of urine.

So, if you want to write a mare being in heat - think about a few of these things.