This book sounds familiar to me but I could be mistaken so I have a few questions. Was this geared toward young adults? The parts you mention about collecting stones, storms and freezing weather, do you happen to remember if those parts were in the very beginning of the book? Also, does the magic he use take lots of hand movements? And it's a coming of age story so probably - but you never know, was there a girl involved there in the plot somewhere? Last one, and this might sound a bit strange, but did there happen to be a part about an important horse in there?
My guess is it's The Ring of Allaire by Susan Dexter. It was written in 1981 and it has all the things you mention in it, swords, a quest, magic. It's the first book in a trilogy but it's not bad as a stand alone novel.
The main character is the orphan Tristan, who is an apprentice of his master the wizard Blais. At the very beginning of the book he's collecting stones by the river for use in magic. He's not very good at it he thinks, so he tries to redeem himself by finding good stones and accidentally takes too long. Then he makes a great find, a feather, and notices the time and hurries home. He sees signs of a magical storm on the way, hail, ice, and damage, and gets worried.
After he arrives home he discovers his master is dead, killed by an evil ice wizard because Blais has come very close to solving the biggest magical mystery of the last few centuries. So Blais' last act is to magically send Tristan on the first step of his quest to finish solving it.
That is a summary of the very beginning of the book and I do believe it nicely includes most all that you were remembering. The rest of the book of course includes Tristan solving the mystery and finishing his quest, but the answers he finds are not what he expects.