You really have to look at the use policies of the various images. There are a lot of different usage license types out there and even if you are not making money, it doesn’t mean you can just use anything under the sun. Sometimes the usage rights are there just to protect the brand. Some brands don’t want you using their imagery with different colors, sizes or in certain relationships to other imagery that may convey an improper message. Just look at Apple. Their apple logo is one of the most protected brand images out there and they can come after you just for putting their logo next to a competitor in a way they don’t like.
I am no expert in these matters, but I have had to wrangle a few corporations in my work as a web developer to make sure that even the colors were the right pallette, that their logo size was even to that of a competitor or even bigger than their competitors in some cases.
Now do I think they will come after you for playing around with design? Probably not. However, you have to stay fully aware of how you are using logos and imagery in the things you put out into the universe… again even if you are not getting paid.
Heck, I know companies who put out internal memos to their employees about how they use their imagery and that before publishing anything, it has to go through review with marketing and brand experts. So again, be cautious and stick to images that perhaps you have a right to use or have permission. When in doubt, just ask. You might be surprised what companies will let you use if you just ask. (Btw… I wouldn’t use any big money brand name imagery if you can, that is just playing with fire)