I was thinking of making a symbol font that would include a few company logos. Would it be copyright infringement (on my part) if I did not use these for commercial use and kept them free to download and use?

Thank You in advance :-)

Yes and yes.

Most logos are copyrighted AND trademarked. So, it's not possible to use it without the agreement of the mark.
But many marks are lenient because they consider it advertising.
This is the difference between the law and usage.