Windows doesn't store (this) metadata in any special place in the filesystem; the Properties window simply reads them from the image file itself.
I don't think .NET offers any functions to read just the metadata from an image without loading the entire image. If you're dealing with only a limited number of different image formats (e.g. only JPEG, PNG and GIF), it shouldn't be too hard to read the size from the image header yourself.
If, on the other hand, you have to deal with many image formats, maybe you can have a look at the source code of the Unix file
utility. It manages to detect the size of many, many different image formats, and is blazingly fast to boot.