how to open .mat file without using MATLAB?

I didn't use it myself but heard of a simple tool (not a text editor) for this so it is definitely possible without setting up a programming environment (by installing octave or python).

A quick search hints that it was possible with total commander. (A lightweight tool with an easy point and click interface)

I would not be surprised if this still works, but I can't guarantee it.

.mat files contain binary data, so you will not be able to open them easily with a word processor. There are some options for opening them outside of MATLAB:

If all you need to do is look at the files, you could obtain Octave, which is a free, but somewhat slower implementation of MATLAB. You can refer to How do you open .mat files in Octave? for more information on the subject. You can get octave from http://www.gnu.org/software/octave/download.html. The interface is very similar to MATLAB's.

As NKN and Ergodicity mentioned, there are python libaries available for this as well.

The most hardcore solution would be to write your own processor from scratch. The MAT file specification is available from MathWorks at http://www.mathworks.com/help/pdf_doc/matlab/matfile_format.pdf.