99 2L golf cuts out while driving
 

I have a 99 golf gls 2.0 and when im accelerating it seems like the gas cuts out. When i let off the pedal and press it again itll accelerate for a few seconds then do it again. And when im at a steady speed it doesnt do it. It doesnt stall, just cuts out. Im in CT and its been very cold recently and it has been sitting until i was able to replace the starter. A friend said it may be frozen lines or water in the gas. Any ideas?