steamsteam-trading-cards
I was level 3 on Christmas sale (Steam), and I voted each 8 hours.
A message popped out, telling me that I'll receive my cards when I reach level 10.
I just crafted another badge, and I'm now level 10, but I don't have any new Snow Globe trading cards.
Am I going to get those cards, or I must wait until next sale / vote?
A few examples:
All Steam seasonal sales so far with ∞ badge levels:
The Steam Winter Sale of 2013 was the first to set the precedent, in which for the first time both foil and regular badges were able to level up as many times possible during the event. This meant that users could easily complete badges and quickly level up their Steam accounts, without a "level cap" on the badge.
A few examples of users with high levels of badges:
From the Steam Winter Sale on out, most of the other Steam seasonal sales feature badges unlimited levels (exception is the Summer Getaway Sale), so theoretically, there's no limit to how many levels you can get with any of those badges.
The "restrictions" you're saying you've got on your account do not match up with what Steam call a "limited account" - it is probably worth contacting Steam support to discuss the issues you're having with the Steam store.
There are four methods of earning Snow Globe cards:
Vote in the "Community's Choice" sale every 8 hours, for every three times you vote you get one card (that's one free card per day)
Buying games/software from Steam: for every $10 you spend on Steam you get a Snow Globe card
Trading with other players on the Steam market
Crafting other badges will result in a Snow Globe card for each badge crafted
One thing to note is that getting Snow Globes by voting for the "Community's Choice" sale requires that you be level 5 already.
Best Answer
The Snow Globe Trading Cards for the Steam Holiday Sale 2013 were explicitly only available during the sale:
The cards have, as such, since been removed from the system and will not be handed out anymore.