Actually, hydrogen in its gas form is too light to be held by the Earth's gravity. Any hydrogen existing as gas would escape from the Earth's atmosphere fairly quickly. Furthermore, even if all the water froze, there would still be other gases in the Earth's atmosphere. The atmosphere is comprised of about 80% nitrogen, 16% oxygen, and the rest is a mixture of other various gases.

There is very little hydrogen in the atmosphere that isn't bound to oxygen to make water, so if the oceans froze, we would still have mostly nitrogen and oxygen in the air.