Should I send a customer survey to all of my customers or a select group?

If your customer base is large enough that you can send a customer survey to a subset and still be certain of getting a statistically valid sample, then you may be able to achieve valid insights without surveying the entire group.

If you are only interested in gaining insight into a particular customer segment, and the segment contains enough members to result in valid data, then it is perfectly acceptable to send a customer survey to only the members of that segment. Segments of interest might be customers over or under a certain revenue threshold, only those who have purchased a particular product, or customers in a specific region.