Processing large amounts of Rasters in R

I have 6500 processed and clipped rasters that indicate snow levels on a daily basis in the northern hemisphere. I need to create a raster that represents a sum of the snow for the season. The winter season would then go from September 1999 to march 2000. I was just wondering how I would go about recalling the daily rasters into R using the loop function/ how i would go about calculating the seasonal sums. Keep in mind that the rasters span two different years and that I don't want to include all 1999 snow data because that would include the previous winter(98/99) as well.