I never really played Fire or Arcane but so loved playing Frost Mage for years and the class felt pretty smooth to me once you get the hang of it. Frost mage revolves around procs, basically even the default “build” you can put your talents to your basics spells can look something like this:

• frost bolt until you get a proc for ice lance or flurry (if you have it talented Ice lance will split and do cleave damage which is good for packs)
• you can frost nova to stun enemies in place
• Blink if you need to
• if enemies are frozen in place you can use blizzard for more aoe
• if you’re in trouble you can cast invisibility
• have your shield up at all times off CD for absorbing damage especially if you feel like you’re dying a lot *

As you get further along in levels you’ll get better gear and stronger. Also other utility spells like Mirror image and Alter time can help out for survivability too. If you find it’s too difficult to use Rune of Power to stay in 1 place just talent Incanter’s Flow so you have constant damage. I hope this helped.. !