Mark me down as a car person too. A well-maintained secondhand Saab, a Hummer II with all the options, or a leased Lexis say as much about a character as a Vizla vs. a Havanese, or a Glock 17 vs. a Desert Eagle .50.
Admittedly, cars aren't a detail that speaks to everyone. Some people just won't notice a car unless it's something like a late-50s DeSoto FireFlite Sportsman, or a Rolls-Royce that's been converted into a pickup truck -- which is no doubt why those very distinctive vehicles are driven by their respective characters.
I'm in favor of specifying make and model, if it's not done too awkwardly or indiscriminately. It makes your fictional world more real and particular. Readers who do get cars will appreciate the extra detail, and those that don't will just skip past that bit.
There's no copyright or trademark issue present. In general, you'll do well to assume that you can mention anything but song lyrics.
I'm guessing that your editor and your beta readers aren't car people. That's their privilege. However, they ought not be chopping out significant details without querying you, or at least noting that they've done it and why. It may not matter all that much if they cut out the make and model of cars in your current work, but if they feel free to delete any details they don't understand, someday they'll delete details that do matter, and then it will be a problem.