I know some writers find it hard to use capital letters correctly; New Hart’s Rules has an introduction to capitalisation you might find reassuring:

Capital letters in English are used to punctuate sentences, to distinguish proper nouns from other words, for emphasis, and in headings and work titles. It is impossible to lay down absolute rules for all aspects of capitalisation … the capitalisation of a particular word will depend on its role in the sentence, and also to some extent on a writer’s personal taste or on the house style being followed.

The most important thing, I think, is to consider why you have used a capital letter – nouns don’t automatically need one.

There are some general principles you can use to guide you. The convention for months and seasons is fairly simple. I have included days and festivals below because they are often queried at the same time.

Days

The names of days are capitalised:

She was born on a Wednesday
Can I visit next Saturday?

Months

The names of months are capitalised:

The referendum will be held on 23 June 2016
I'm going on holiday in April

Seasons

The names of seasons are not capitalised:

I like to visit the beach in summer
There was a distinct lack of snow this winter

However, you should use a capital letter if you have personified the season:

And Winter shook his frosty mane
The warm sun ended Spring's slumber

Festivals and holidays:

The names of festivals, holy days and holidays are capitalised:

We are preparing for Ramadan
I don't like Halloween
What are you doing on May Day?

If you would like more information on using capitals, I recommend starting with Trask’s Guide to Punctuation. If you would like additional guidance, New Hart’s Rules is a useful style guide for UK publishing and is fairly thorough on the topic on capitalisation.

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References:

New Hart’s rules: the handbook of style for writers and editors (2014) 2nd edn. Oxford: Oxford University Press.

Trask, R. L. (1997) The Penguin guide to punctuation. London: Penguin Books.