I'm on my second Nightmare run. First one was as a mage, and this one is as an Archer. If you play either of those classes, bring two warriors built for sword & board. Make sure the mage has barrier (duh). On my current Archer, I just set the two warriors loose and let Vivienne keep them buffed. I disabled all her other spells except for Winter Grasp and barrier. She usually buffs the two warriors, then freezes someone. I shatter that target with longshot. In most battles, nobody touches me and Vivienne.
Weapons and armor are huge, so make sure you're always crafting or buying upgraded stuff. For instance, my goal was to go after the unique bow you get for doing all the astrariums in the Hinterlands. Also, don't save money. I did in my first play, and it only made my early game harder. But the end I was swimming in gold and had nothing to spend it on. Feel free to blow coin on good gear in the early and mid game.
For rifts, make sure you have two people who can dispel. Cassandra gets this after Skyhold, and all the other mages have it in the spirit tree. Set the mage so that he/she will have 50% stamina reserve, and disable "dispel". The moment you have killed the first wave of rift demons, get your party into place around the rift. When you see the blue dots appear on your minimap, you have a brief window to cast dispel. Your targets will show up on the ground as red enemy circles with no enemy (yet). Cast, then use the right trigger to advance time. This will close the portals and eliminate a chunk of demons. You might not find it necessary to do this on all rifts, but those ones with terror demons can be hellish.
One tip I can give you for the Trebuchet is to hang back at first, right around the bottleneck. Use your archer to lure enemies to you. This prevents the mob from swarming. Bees help also. They'll come in waves, so save after each one, and don't use the supply cache until you're all out of potions.
After Skyhold, you'll have Vivienne as a Knight Enchanter, so when things get really rough, fall back on her. KE isn't quite as OP as people might have you believe, but when played properly, she can be a lifesaver.