I have a shower in the basement (two knobs 1.cold 1.hot). At 6am the cold water trickles but at 9am the cold water works fine. Hot water is just fine.

Any ideas would be greatly appreciated.

Do you have a water softner that could be recharging every day at 6:00 AM? I'd be surprised if a softner was recharging every day, but they do so on a periodic basis and they use cold water. Although I can not imagine that it would use enough water to cause the basement shower to trickle, maybe it can. Is the cold water in the rest of the house OK at 6:00 AM?

The rest of the house is perfectly fine. I believe it's copper piping but I don't think it's frozen.

The rest of the house is perfectly fine. I believe it's copper piping but I don't think it's frozen.

I agree that the pipes should not be frozen. Not sure if your basement is heated, but if it was cold enough to freeze water, there is no way you would be showering down there.

Is this a stand along home, or a townhome type situation where you may be sharing water lines with neighbors?

I am just pulling stuff out of my butt here as I am the farthest thing from an expert you could find, but maybe something will help :-)

Three questions:

Are you using city water, or on a private well system?

Does your setup have a "booster pump" anywhere?

Do you have any major whole-house water-related appliances? (e.g. water filter, water softener, etc.)