Find the northernmost entrance to the mountain from either Catherby, Taverley or take the gnome glider there and run north. Mine the rubble out of the way (requires 50 Mining and a pickaxe), and take the southern ladder. Follow the southern path in the caves until you see a reachable ladder. Climb up that one, and you will appear back on the surface. Then, take the eastern ladder. Follow the upcoming path (littered with ice giants and ice spiders) until you see another ladder. Take that ladder, and from the surface, the ladder next to it. Follow this final path to the Ice Queen's chamber room.
Warning for lower leveled players: her lair is a multi-combat zone and she is surrounded by level 57 ice warriors who will attack you.
She has a weakness towards fire spells so it is recommended you use these if you have a decent magic level.
She is not immune to poison - so this can be used as a way to drain her health if you are otherwise struggling to damage her - see below for a hiding spot to heal and wait for poison to do damage.
There are areas of her cave where she and her minions cannot walk, limited by their patrol range - these areas (behind clumped icicles pointing up from the ground) can be very useful to take a break to eat some food, and can even be used to safespot the queen if used correctly.
An example of this is shown in the images below - to the eastern side there is a clump of icicles, behind which the ice queen and warriors cannot reach. Use this spot to heal up, and also it can be used to range or mage her for the safety of this spot! You may have to 'hit-and-run' to lure her closer to the spot - firing at her then running closer to the spot until she is within firing range of it - from which you may chip away at her to your heart's content.