Many radio stations offer free Christmas music online, sometimes as a live broadcast, and others as a recording. Check to see if local radio stations in the area offer this service by logging onto their websites.
There are several websites that offer continuous, free music that can cater to the musical tastes of the listener. For example, pandora.com allows the user to create unique "stations" by specifying the artists, songs or genre(s) desired, then automatically matches these to songs that have similar characteristics, and adds them to the listener's stations. The listener is able to continuously modify the stations and add or remove songs at will.
If none of these options is appealing, there are many search engines, like Google, that can be used to find other music streaming websites, some of which may require installation of media players. If a particular type of holiday music is desired (Christmas Oldies, Traditional Christmas Carols), it will help your query to specify this in the search parameters.