A. "When forty winters shall besiege thy brow,"
B. "And dig deep trenches in thy beauty's field,"
<u>In these first lines, Shakespeare uses "forty winters" to call up the pain and cold of winter, just as if you were aging. Forty winters also means forty years. </u>"shall besiege thy brow" is referring to back in the day, when someone would dig a trench and wait, attacking continuously over a period of time (lay siege). <u>So he is comparing this youths brow, or forehead, to the wall of a castle being attacked over a period by time and old age. </u>
If you dig a trench in a field it will not look the same, even if you fill the dirt back in it will never look like it did once before. <u>Time, age, has dug trenches into "beauty's field" the beauty of youth, and that is something that will never return.</u>
Sorry this answer is late, but I'll put it here for anyone still looking.