I guess that the surface area of the nut may be a factor in such cases. 

Let's take the walnut: being sort-of medium-sized in overall form; but due to its "wrinkles" and "wings" has a huge surface area relative to its mass. This may be important for the purposes of needing to have its dormancy broken first by prolonged cold/winter (but not freezing) - known as stratification; and then by damage - known as scarification.

For both requirements, the "wings" and "wrinkles" may serve as heatsinks - or coldsinks - enabling the seed to reach and maintain itself within the required temperature range (hot or cold) as effectively as possible (based on its surroundings), through as much of the seed as possible. Likewise in needing to undergo scarification also, it is to the advantage of the seed to be damaged (maybe nibbled by a squirrel! for example) but not damaged so badly that there is not enough of the seed left to supply energy to germinate and grow seed leaves and roots. Also, if the part of the nut that houses the germinating part of the seed is deep in the centre of the nut, then having the rest of the nut around it protects the centre of the nut, and considerable damage to the outer regions of the nut are basically expendable if they ensure the survival of the heart of the seed. The seed needs to be viable to begin with though!