Black and white photographs usually demand either a black or white or silver frame. To introduce a colour into the frame or the mount only distract the eye and the viewer sight will be drawn towards the colour before the photograph and this is not good framing practice.
A good picture framer will be aware of how the viewers eye behaves when looking at an artwork. The last thing you want is the viewer to admire the frame and not the artwork! Although that can often be the case!!!
The coolness or warmth of the photograph will have to be balanced or countered with a white mount that is either warm or cool in tint. White mounts come on a complete range of tints from pink in the warm range to blue in the cool and it will be a matter of testing each one against the photograph to get it right.
Colour photographs can be framed in coloured frames. The quality of gloss or mat finish of the photograph will dictate the type of frame. Photographs can be framed in many individual ways by floating or surface mounting is not usual.