My dracena's leaves start to turn brown at the tip, and eventually the whole leave is dry and dead. Help! I don't want to lose it.

I mist it every morning. It gets indirect light from a southern window. I water it once a week. No fertilizer. it is about 3 feet tall. It was outside all last summer, and may have gotten too cold in an unexpected October freeze (it was in the garage).

Can I cut it in half and hope it will regrow?

What kind do you have? A pic? Would it be possible to give it rain/melted snow, or distilled? Tap water chemicals (and usually also wrong PH) can make these ill.

Brown edges can be caused by too much salt build up in the soil and also from flouride in tap water. Using distilled water might help but also be sure that when you water, give the plant enough water so that it saturates the soil and runs out the drain holes. Never let a plant sit in a tray of water for very long or you will end up with root rot.

Dry, brown leaf edges can caused by too little humidity; misting helps but sometimes it's not enough especially during winter when folks have the heat on which can dry plants out pretty quickly. You can place the plant on a tray of moist pebbles which raises the humidity around the plant, adding a wee bit of water to the pebble tray as it evaporates.

What she said.

Could be other issues, but most common would be the humidity issue (or lack thereof). You can also stick the whole plant in the shower every now & then and just let the water run over it (pot & all) for 10-15 minutes. This helps wash out build up of minerals & salts from the tap water that can eventually cause problems. Plus it gives the plant a nice bath to get any built up dust & dirt off the leaves.