is it ok to give a labrador a bath with an outdoor cold water faucet?

As long as the dog isn't overheated and the water is super ice cold it should be fine. My boys are always standings vet the sprinklers letting the water soak them down so they don't seem to mind the water temperature. You can try running water over the dogs hind end and see if the dog to,erases it. Some dogs like the cold some are indifferent and others avoid it. It won't hurt your dog if you try wetting down the hind end, if he hates it right away you will know.

I have started bathing several of my dogs out on the patio, they don't seem to care that the wasters cold, I just set them down, rub in the diluted shampoo all over then rinse. They love it! My smaller terriers don't have the same appreciation for cold water as most of the other dogs do, they prefer their baths warmer. The terriers are also the dummies that lay out in the sun in 100 degree weather panting hard but sunning themselves, they refuse the wading pool or the shade preferring the warmth of the sun, that's why they are so limited and supervised when they are outside, they are like kids... ' it's not too warm!' Lol. They always hesitate coming in when I call them.

Yep!

Labs are anyway renowned to be very fond of water, be it dirty water, or clean water!

Though shampoo is not such a good idea it will wash away those very important oil secretions that protect your dogs skin. It really needs those oils to waterproof and lubricate it's skin...

The ole Lab gundog my parents had years ago. I trained her (Jenny) to the gun, during her training on rough shoots i used to take Jenny over the moors and bogs of Exmoor for sometimes days at a time.

She really loved to be brushed under the hosepipe when we came home covered in Mud and Peat and because i never used shampoo the oils remained on her skin and coat as nature intended they should.

Jenny never had a skin problem in her life either,,,It got to a point where she would run ahead and wait under the standpipe for me to arrive. the only time she would not wait at the standpipe was if i had shot game in the bag.

She wouldnt leave that until she saw that it was safely hung in either the pantry or the cellar.

If you don't like bathing in cold water, then your dog won't like it either.

of course ,if you like .