We had our first real mountain holiday earlier this year, after learning and riding in the domes. As mentioned earlier, hydration is key, and bring snacks if you like. If you get tired, take a break and enjoy the scenery. Don't feel pressured to keep riding nonstop or you'll be knackered the rest of the week. Like Neni said, we found day 3 to be the worst in terms of soreness. Bring some paracetemol or something and you'll be fine.
We actually found coming back to the domes was more tiring in a short time since you're constantly on the lifts. If you're relaxed and just cruising, that takes a lot less effort than skating around and riding the pomas. Try to stick with blues and reds at first - greens are super easy but tend to have too many flat areas that we boarders struggle to keep enough speed, and end up skating a lot which is very tiring. And we didn't even consider black runs at all, way too scary! An instructor in our group ended up sliding on his bum halfway down a black because the conditions that day were so icy.
Real snow will ride a fair bit faster than dome snow, but you also have a lot more space so I didn't find it that big of a deal. If you're concerned about speed, it might be worth looking at a lesson early in the week to make sure you have the correct technique, though with lots of dome lessons you're probably good there. Tips on carving would be handy. The first few drop ins at the top of the mountain will be scary as heck, but you get used to it quickly and you'll find yourself picking up speed as the week goes on.
Chair lifts are easy to get on, no problem there. Getting off can be tricky, but if you can slide out of the way as the chair swings round, just stop and take your time skating away. It just takes practice like everything else. I've not had the questionable pleasure of trying t-bars, but button/poma lifts are just like in the domes, just much much longer.