You can make custom colour patterns in Inkscape. Draw a pattern, using as many colours as you want. Select all the pattern, then do Object > Pattern > Objects to pattern. Now you have a colour pattern.
As for colouring the standard Inkscape patterns, you can use the Colourise filter. Filters > Colour > Colourise. This filter works in browsers when viewing SVGs. Tested in Firefox and Chrome. This is a pretty easy solution, but filters won't work for everything - only for software which is capable of rendering them.
Here's the SVG
It's also possible to edit the fill of an object inside a pattern (since these are just ordinary SVG objects), but you'd need to go into the XML Editor to do that. There's no way to alter it from within the normal Inkscape GUI. You'd go into the svg:defs, locate the pattern id, and find the object within it, then change the fill from black to whatever you want - in this example the object is an svg:rect and the fill set to #ff0000. This is certainly the most efficient solution, as there is no reliance upon software's ability to render SVG filters.