I was wondering if a nose cone on a b1 would provide better, not as good or the same cooling than the factory low water pickup?

Same as before as long as you keep open the same holes. The cone doesnt change height etc.

A nosecone will cover the LWP holes. You will need a standard side pick drive or DWP drive. You would have to plug the LWP holes on a DWP drive.

The LWP is a force feed situation.. The faster you go the more it water is pushed in. With a cone and no LWP, the side pickup usually pulls in a sufficent amount of water. Channeling can be done to help increase it and depending on what cone you use, it may or may not feed those side vents..
On the other hand, anything in front of the bullet can cause turbulance to the prop.
So to answer your question.. I think LWP would force more water through the drive than a side water pickup with a cone. But it can be different for different situations..