For the benefit of others (and if you don't already know), what's happening to your roof is what's known as Ice Damming. To answer your question, you could knock them off BUT, if you think that in doing so you'd damage the roof/shingles, then I wouldn't do it. What's important for others (and you) to know is that the cause needs to be 'addressed'.
What you described in less than 25 words is bad news. You say you can't do much about this but actually, you can do some things. If you're interested in some insight other than what's provided in the above links, post back with more information about your house and ask whatever questions you'd like. In short, if this continues unabated, you'll be asking 'us' how to replace your roof and/or how to stop the 50+ leaks in the house. All this expansion and contraction WILL be 'noticed' in a matter of time. I do wish you well. (You know where to find 'us' ...)