Learn Swedish: Vi har mycket snö på vintern. - We have a lot of snow in the winter.

Because snö (snow) is an uncountable noun. You can measure it, but you cannot count it (you would not say "one snow, two snows"). Swedish uses mycket (much / a lot of) for things we cannot count, and många (many / a lot of) for individual things we can count.

The English translation says "in the winter", so why does the Swedish sentence use the preposition på?

When talking about things that happen habitually during a certain time of year, Swedish uses the preposition på. Therefore, på vintern is the standard way to say "in the winter" or "during winter".

Why does the word vinter have an -n at the end here?

When making a general statement about what happens during a season, Swedish uses the definite form (which is like adding "the" in English). Vinter means "winter", and adding the -n at the end makes it vintern ("the winter").

Do I need to pronounce the t at the end of mycket?

In formal speech or reading, yes, but in everyday spoken Swedish, the t at the end of mycket is almost always dropped. You will usually hear Swedes pronounce it as "mycke".