I redesigned my resume using InDesign and this modern resume tutorial.
However, I'm wondering whether I need to redesign my cover letter as well since it might look odd if I email my beautiful resume (pdf) and a bland cover letter created with Word. My question is, should I also create a cover letter in InDesign as well? I'm not a designer. I'm applying for a programmer position. Thanks in advance.
If emailing... the email is your cover letter. It should NOT be designed. Well, at least not to any real degree. I, personally, prefer plain text emails, so if I get an HTML email.... it's ignored as spam for the most part.
The purpose of a cover letter is to get the potential employer to look at your resume. If you add the cover letter as part of your PDF, you've completely ruined the purpose of the letter to begin with.
Put the body of the cover letter in the actual email you are sending, not in a PDF.
There is generally nothing wrong with including the cover letter in your PDF in addition to putting it in the body of the email. But you should not expect anyone receiving an email to open a PDF to view your cover letter.
Adding to Scott's answer, sometimes (if you are applying through a portal that saves your information, for example) you might be asked to upload a cover letter file, separate from your CV.
In both cases I think the best option is to go for simple. Depending on what your CV looks like, you could re-use some styles from your resume (titles, body font). But I wouldn't design a cover letter, the attention in this case should be in the content and not the container.