As Isaac states this is not possible with the search tag. I know you were giving an example of the syntax you would like but the search doesn't work in this way.
I think you may need to approach the build in a different way. It seems like you would like to filter results based on certain fields. EE doesn't have any real solution for this as standard. It has been achieved before by using either SuperSearch or Low Search. John Henry gave a great talk at EEUK using SuperSearch in this way so it's possible but complex.
I have built a product store before and used Low Seg2Cat to great effect. Create category groups for each of options you'd like to filter the entries by. Then use Seg2Cat to map the category_ids from the url to the entries category parameter.
You can do this using the magic {segment_category_ids}. It also won't matter what order your segments are in but setting out a standard structure would be a good idea. Also you'll need to restrict your category options to unique names.
Eg.
Set up 2 category groups:
colour:
collection:
- collection a
- collection b
URL: example.com/products/red/collection_a/
In the index template of 'products' template group:
{exp:channel:entries
channel="products"
dynamic="no"
category="{segment_category_ids}"
}
{segment_category_ids} will contain a pipe delimited string of the category_ids from the url segments, like: 2|45|4|9
In this way you can filter your entries based on the url.