There are a many ways (how could I count them all?) to promote your patterns without having your own website/domain.

Online Art and Crafts Communities and Marketplaces

A number of sites exist to promote artwork, including:

Zazzle

Cafe Press

Threadless (t-shirts--will your designs work on them?)

Etsy

And don't forget:

eBay

Craigslist

Communities and Forums

You can also sign up as a member of many online communities and forums that focus on sewing, crafts, quilting, or any other creative endeavor that might use designs like yours. By getting involved in the communities with an honest intent to share information, you will gain a reputation as a trustworthy authority, particularly if you specialize in answering questions related to your interest, in this case textile design.

This may be a slower way to market, but it's highly likely that the people who do show an interest in your work, via these online communities, will be targeted prospects for your wares. People you build a relationship with will often be your most loyal champions.

Manufacturers

If you're more interested in selling your designs to manufacturers, you might simply start searching the Web for textile or fabric manufacturers.

For example, here is a site that lists many:

Global Sources

Contact a company representative through the site contact information, which is almost always included. However, if you decide to take this approach, make sure you have done whatever you can legally to protect your designs from intellectual property theft. You should talk to a good intellectual property (IP) lawyer before making any deals.

Best of luck to you!