You should queue inputs. If you press left-down the snake should turn left and then go down on the next frame. That is, if you are attempting to recreate the classic Nokia experience, anyway.
Wow, it is interesting that "the reference" for the snake game is the one in a Nokia mobile phone. The reference for me is the BASIC implementation that (I think) came with a version of Microsoft DOS some time ago.
I guess the nokia implementation is considered the reference because it had the install base and must have wasted hundreds of thousands of hours worldwide.
IIRC the DOS version was pretty much unknown unless you happened to scour your disk for .BAS files.