WIP - Pixel Art Map (Help with Rivers?)

[BindTortureIll]

I've started myself a pixel-style map of a fairly generic fantasy setting, climate-wise. Other regions will have more interesting parts like jungles and deserts and the like, but for now we can assume that everything is England, just like in most fantasy. The red dots are markers for cities, eventually there will be an easier way to name them. I've thought about doubling the image's size to give myself a little more room to work with. Light green is plains, dark green is forests, blue is water, black is just for outlines at this point.

I have a bit of an issue regarding rivers. I know what rivers can and cannot do, that they will generally end in the ocean and never flow uphill, but I don't have a very firm grasp on how rivers tend to work, especially as they get smaller. The river flowing through the lower forest are barely larger than creeks, as I've been building the forest around them. How much rain does there usually have to be before a river is formed? I know that rivers tend to have winter and summer cycles, the snowmelt powering the former and rain powering the latter, but how do rivers last without constant rain over them?

On a similar note, is my idea sound that forests would generally grow where there are abundant creeks and rivers to support them?