If a bank makes a social media post for example "check out our mortgage services" and includes a link to their mortgage site should the equal housing logo be included?

I believe so. Perhaps when a veteran replies take that info and run with it.

From 338.3 of the FDIC's rules:
(a) Any bank which directly or through third parties engages in any form of advertising of any loan for the purpose of purchasing, constructing, improving, repairing, or maintaining a dwelling or any loan secured by a dwelling shall prominently indicate in such advertisement, in a manner appropriate to the advertising medium and format utilized, that the bank makes such loans without regard to race, color, religion, national origin, sex, handicap, or familial status.

Your ad is "advertising" a loan "for the purpose of purchasing, constructing, improving.... etc," and therefore, is an advertisement subject to EHL rules. The EHL rules don't address links and web ads as the rules were written before that technology was around. Therefore, it is best to include it.

While not law, you could review the FTC DOT Com Guidance from March of 2013 which gives guidance for a "one-click" rule. That said, it is always better to include the EHL - which is my recommendation.

Any electronic channel used for one-way broadcasts of information about bank products and services should be treated as an advertisement for any and all consumer protection regs unless there is a specific exclusion. What you describe is a billboard with a hyperlink.

You rock Adam and Richard