What others have said about clothes is right, comfy trousers without prominent inner seams, shoulders covered, good bra (and I would add comfy pants, a riding wedgie is not a good look!), sensible shoes, no trainers or wellies (your riding stable may be able to lend you riding boots if you don't have anything suitable). Make sure to tie up long hair and remove any jewellery especially dangly earrings!
In terms of what to expect, your instructor should come and meet you when you check in, fit you with a riding hat and check you are safely clothed. They should also ask about your previous riding experience (none is fine!) and aspirations - e.g. are you ultimately aiming for your own horse, do you want to hack out. They may ask (if this wasn't asked at booking stage) for your height and weight - don't be offended, this is to match you with a suitably sized horse.
They should then take you to meet your horse who will normally be the quietest/safest the stable has to offer, and may seem very sleepy/lazy and reluctant to move, esp in this weather! This is fine and what you want in a beginners horse. As you get more experienced you can ride some more lively types.
You will be taken down to the enclosed area (called a school or menage) where you will ride. Some teachers like to do a short safety briefing and explanation of the basics (how to stop, go, steer etc) on the ground first, others will get you straight up and explain from there, either is fine.
For your first lesson someone else should be in control of the horse so you can focus on the basics. This will be either a 'helper' (who may be a teenager volunteering!) leading the horse on a lead rope walking beside you, or the instructor may use a 'lunge line' (a long line attached to the horses bridle, they stand in the middle and the horse walks in a circle around them).
In your first lesson I would expect you to get comfortable at walk, work on getting your legs, hands and seat into the right position, learn and practice the aids to stop, start and turn. Then try a trot and learn the art of 'rising' to the trot. This will be difficult and uncomfortable at first, don't worry, everyone finds it hard but everyone gets it within a few lessons at most, some much quicker than that!
Your instructor should take things slowly and at your pace and you shouldn't feel nervous or unsafe at any point. Horsey types can however be a bit 'gung-ho' in personality so if at any point you feel uncomfortable, want to stop or simply need something re-explained to you, be sure to say. They won't mind!
You will probably feel fine immediately afterwards but have muscle aches in the evening/next day, even if you are generally fit and strong. Again normal and it passes, riding uses quite a different set of muscles to other kinds of exercise. A hot bath will help!
Enjoy and report back!