*Music starts* (Bo-wemo-way Bo-wemo-way Bo-wemo-way Bo-wemo-way) In the Ice caves, the frigid Ice Caves, Snow-a-ger sleeps tonight. In the Ice Caves, the friged Ice Caves, Snow-a-ger sleeps tonight. (A-weeeeee-eeeee-eeee-eeee-a-weema-bumba-way!) *Music fades*
Yes, it is possible to get stuff from Snowager while he sleeps. He sleeps three times a day. Those three times are 6 am (to 7 am), 2 pm (to 3 pm), and 10 pm (to 11 pm) NST. NST is displayed on the Neopets main page in the right-most column, just below the words "Latest News". Or, you can go here to find out what time it is currently in Neopian Standard Time (NST).
If you live in the US, I can convert NST into your time, based on your time zone. (You can do this for yourself if you live outside the US, by finding out what the current NST is and finding out how many hours different it is from your current time.)
When you try to steal from Snowager, one of three things will happen. First, you could succeed and steal an item. It could be a worthles 10 NP item, or it could be valuable. You never know. The second thing that could happen is Snowager could move as you creep up for your gift and you run away in terror, chicken-hearted as you are. This happens about half the time. The last thing that could happen is that Snowager could wake up and blast you with ice, chilling all you pets down to zero remaining HP. If this last thing happens, I recommend a free visit to the Healing Springs in Faerie Land. You can return every 45 minutes to have your pets healed for free, so return often. You can sometimes get free healing items, too.
Snowager is one of the most profitable parts of Neopets. Just remember, what goes around, comes around, my fellow theives. Eventually the Pant Devil (who I think is in league with Snowager and that's how Snowager gets all his stuff) will come to steal from you. Don't get too mad at him. :)