direct link to an online app that's only offered to select customers, so rather than just sending out a plain text link,
Great. I have two questions. What are you going to do for those customers whose email providers only allow text emails? Sometimes it has nothing to do with what app the user is using to check their email. Or what about those clients that have purposely configured their email apps to allow only text emails?
It is possible to embed html directly into an email. A couple of problems with it though. Use of images also allows for people to track whether or not an email was opened, which can be a privacy issue. Also, it is popular for phishing emails to contain large amounts of HTML. What that means is that filtering software often pays more attention to HTML emails, and is more likely to flag them as spam. If your client uses Hotmail or .... can't remember the other one right off the top of my head, anyway, if the HTML does not comply to W3C standards, they will reject it.
Just a few things that you should consider. Otherwise, there are tons of tutorials that show how it is done. However, if any of the conditions I listed above exist, then your email won't make it anyway, or will be unreadable.