Yes, products intended for the face and body should be properly preserved. Unpreserved skin care products carry the following risks:

 
Topical bacteria growing in the product (and then transferring to the skin causing serious infection)
Active ingredients breaking down prematurely and losing their effectiveness

Preservatives should only be used in very low percentages. In most of our products, preservatives only make up 0.5% of the ingredients. Due to these low percentages, our products do not have a shelf life of much more than 18 months, whereas many many in the industry have a disturbingly long shelf life of three or more years.

In order to properly preserve a skin care product without using chemical preservative, one would have to use an excessive amount of alcohol - probably at least 30% or more depending on the lipid content. Lipid or oil-based products require more stringent preservation as oil tends to break down more quickly than water-based ingredients.