Assuming you use SharePoint 2010 this really is a non-issue:
When the user uploads the picture using the GUI, SharePoint generates 3 thumbnails with a max with/height (depending on portrait or landscape) of 144px (actually 104px if picture is square), 96px and 32 px.
The thumbnail pictures are saved in the User Photos library in MySite host site, and used for different previews around the site.
Hence the original picture is not used at all.
If you instead use PowerShell to add pictures directly to the AD and import them, the cmdlet wont accept pictures larger than approximately 10KB (the AD field can actually hold pictures up to 100KB). After synchronizing you need to run the cmdlet Update-SPUserPhotoStore to convert the images temporarily stored on MySite host to the above mentioned thumbnails.
PS: when all the above is said, a picture of 1 MB is way way too much for a small profile picture!