does anyone run with water bottles?

I started my training yesterday- i know 2 weeks later than planned.

But I did 950 yrds on my eleptical machine, 3 miles on my bike then got up early this morning and did a 1 mile run. ( not too bad for my first couple days and weighing 240lb-huh?)

It was 24* and I don't think I'm breathing right either, my mouth was so dry after the ride and run I couldn't drink enough to get hydrated.

Do you run with a water bottle?
Does anyone run with a fancy 2 bottle water belt?
Do you run with your mouth open?
Do you breath in your nose and out your mouth?

This is the hardest part for me & the Tri training. My wife thinks I'm pushing to hard but I want to be able to run 3 miles by March, If I can't get over the cottonmouth Its going to make the training harder.