Google's John Mueller said on Twitter that Google uses the canonical page for the search results snippet in Google - and often that is not the AMP page.
This comes when someone asked "what is the maximum and recommended meta description characters for AMP pages?" The answer is, this question is not applicable.
John replied, "AMP pages aren't used for the snippet -- only the canonical pages are used."
Of course, the follow up to that question is, what if the AMP version is the canonical version. What if the site is only published using AMP and there is no alternative version?
I am not sure why John did not reply to that specific question - because it is a good one.
I have to assume Google will use what is on the AMP page for the snippet in that case, but I guess someone can test it and see how Google reacts? Update, I should have mentioned that someone outside of Google's own AMP blog should test it, because the AMP blog is only built on AMP and they handle snippets fine.
Update: John Mueller does clarify if AMP is the only source and is the canonical, then they do use it for snippets:
@akinyemi_alamu Standalone AMPs are their own canonicals, that's what we'd use in search.— John Mueller (@JohnMu) November 7, 2016
Forum discussion at Twitter.