For some HTML mails, it is sufficient to use a mailcap file in combination with lynx or w3m:

  # ~/.mutt/mailcap
  text/html; w3m -I %{charset} -T text/html; copiousoutput;

  # ~/.muttrc
  alternative_order text/plain text/enriched text/html  # save html for last
  auto_view text/html

If you want the full HTML experience, you can use this script [1], which uses python (there also is an older bash version) to convert the mail into standalone html to be viewed inside a browser.

  # ~/.muttrc
  macro index,pager M "<enter-command>unset resolve<enter><clear-flag>N<enter-command>set resolve<enter><pipe-message>viewhtmlmail\n" "View HTML in browser"

1: https://github.com/akkana/scripts/blob/master/viewhtmlmail