I would think that, ultimately, it doesn't really matter all that much (if they haven't specified), as long as it's a formal cover letter.
However, personally, I would never put my cover letter in the body of an email. I'd do what one poster said up above and attach the formal cover letter to the email, but include a short paragraph in the email indicating what I am applying for, what documents I have attached, and perhaps one reason why I'd be a good candidate for the position. I would also definitely, definitely include my full contact information in the email itself, as well as on the cover letter and in the resume.
Speaking as someone who processes all the resumes for my department, my favorite applications are the ones that have the brief email statement with all contact information (so it's easy for me to record their pertinent info), but attach their cover letter, resume, etc. as a single .pdf document. My department distributes resumes electronically, so if they attach 5 different files, I have to compile them into a single .pdf anyway. Bonus points if the applicant has vague names for their files and/or attaches them in a strange order (i.e. resume then cover letter).
It's not a problem to get multiple documents, or Word documents, or cover letters in the body of the email, but it does annoy me and increases the odds that their application materials won't present well. I include all emails anyway, and I have Acrobat Pro (which means I can compile various document types into a single .pdf relatively quickly). So a cover letter in an email will still be present, but it never looks as nice as one that was sent as a separate document.
A few other tips, since you are emailing your resume (at least) as an attachment:
- The best way to name the file is with your name (first initial and last name is usually good, to save on length) and be sure to include what the document is (i.e. "JSmith Resume" or "GJones Cover Letter").
- Make sure that you don't have any stray blank pages, because that is either something that somebody has to take out, or it gets left in and potentially works against you.
- Color can be a really nice touch on a resume, but make sure it will still look okay if it's printed in black and white
- Send it as a .pdf if at all possible, unless you can be reasonably certain that the person receiving it has your word processing software. It's a relatively safe bet that a business has Word. It's somewhat more rare that they have Pages (unless the industry is one that tends to use Apple computers heavily). It's annoying for me when I have to ask candidates for a position to send their materials in a different format, and I'm sure some employers just ignore any applications with documents they can't open.
- Make sure your email address shows up with your first and last name (i.e. "John Smith <firstname.lastname@example.org>"). It's really hard to find an email from someone who has not done that.