As of early 2017, counterblock (which is used by Counterwallet) downloads PNG images of up to 20 kiB (20480 bytes) in size and 48x48 dimensions.
This is not a protocol limitation, but just a way one implementation does it.
Another wallet could impose no limit, or a different (smaller or larger) limit, but not that any user using a different wallet (such as Counterwallet) may not be able to see images larger than mentioned above.