Jennifer - Gracie (Lab or as we call her "The Blab" cuz' Huck has imprinted Basset characteristics on her) doesn't seem to have this problem. In fact, I rarely have to even clip her nails as she wears them down herself. W/Huck it's almost like hang nails but it's actually a layer that comes off - not the whole nail but partial.
Given your location this may not be the cause but in winter the air is ussually dryer and adjuncts to deice driveways, street and sidewalks can dry out nails and make then this way.
Omega 3 & 6 fatty suppliments may help but care must be used. If over supplimented or not in the correct ratio more harm tha good isd often the result. It is best to consult with a vet first and better yet one specializing in dermatology.
Brittle nails in Lab
"The best bet is probably to supplement with omega n3 fatty acids. This is usually done using fish oil (3V Capsules tm) and giving 180mg/10lbs of body weight per day, which is a pretty high dosage. For just dry nails a lower dosage might be helpful but for the condition discussed next you would need the higher dosage"