I was wondering if the names of the seasons should be capitalized.

The names of seasons are not usually capitalized.
I love autumn leaf colors.
Today is the winter solstice.
In the springtime the crocus are the first flowers to appear.

They would be capitalized when personified.
Then Spring—with her warm showers—arrived.
Old Man Winter

They would be capitalized in a title.
All City Elementary Autumn Open House

Style guides disagree on which words to capitalize in a title.
Here is one that is a variation of the Chicago Manual of Style rules:

1. Always capitalize the first and the last word.
2. Capitalize all nouns, pronouns, adjectives, verbs, adverbs, and subordinate conjunctions (“as”, “because”, “although”).
3. Lowercase all articles, coordinate conjunctions (“and”, “or”, “nor”), and prepositions (under five characters).
4. Lowercase the “to” in an infinitive.

The U.S. Government Printing Office Style Manual offers one easy style:
“Capitalize all words in titles of publications and documents, except a, an, the, at, by, for, in, of, on, to, up, and, as, but, it, or, and nor.”
[from Writers.com]

Here are some sites for further exploration:
Writer’s Block
eHow
AdminSecret (cheat sheet)
Writers.com

When to capitalize family names such as, Grandma, Grandpa, Mother, Father, Uncle.

Capitalize grandpa when it substitutes for the real name:
  Let’s go to Grandpa’s farm today.

Capitalize grandpa when followed by a name:
  Let’s go see Grandpa Bill.

Do not capitalize grandpa when it could refer to anyone:
  There are many grandpas at the retirement home.

Do not capitalize grandpa when preceded by a pronoun:
  I will go see my grandpa today.