The International Residential Code has a roof rafter to ridge board item under the nailing schedule at IRC R602.3. It's item 7. The purpose of these nails is to transfer vertically oriented lateral load when there's more load on one rafter than on its twin. The language typically used is "unbalanced load." Snow drift and wind cause this loading to arise.
Excess demand on these nails probably contributed to the board splitting like it did. In that case, the capacity of these nail groups has diminished significantly. I'm not at all offended by the idea of depending on a deformed nail to still retain its full strength. I am, however, skeptical of verifiably restoring a nail's strength contribution after bending and splitting.
Optimistically assuming that there were no nails in the failure plane, there's still more bad news. There's also an issue of load paths between nails on opposite faces of the ridge board. If one side has 3 nails above the crack and 1 below but the other side has 1 above and 3 below, then the load has to move across the crack if all of the nails are going to fight their part of the loading. To design your proposed patch under the optimistic assumption, you would decide upon a worst case scenario for any obscured nails above and below the crack and bridge the crack with sufficient strength to carry the load across the crack.
Renailing the rafters to the ridge board is probably the easiest solution. If the entire nail schedule's nail count for both sides of the ridge board were installed entirely above or entirely below the crack, then you would still have a nice load path between each lightly loaded rafter and its heavily loaded twin. That's just the easiest way to state this solution pattern, though. Fixing upon a particular option from the nail schedule, toe nailed 3-10d common nails, for each pair of rafters, you need the same nail count above the crack on each side (2 above on each side, for instance) and the same nail count below the crack on each side (1 below on each side to complete the "2 above on each side" instance). In this configuration, each nail has a peer with identical strength on the other side of the ridge board, so there's a clean load path for its part of the necessary strength.
For your problem, I would treat any obscured edge nails as non-existant. For any toe nails that are more than, say, 1" from the split, I would treat those nails as still good and record their type ("10d common," for instance). I would then buy the recorded type nails (assuming that they're all the same type) and implement the count from the nail schedule's item 7 for toe nails under the recorded type.
This sort of solution is only worthwhile if there's otherwise no need to remove roof sheathing. Without the sheathing there, this is pretty easy to fix without involving an engineer. You can just replace two rafters worth of ridge board at a time. I would first cut away an alternating pattern of the ridge board. Two rafters worth stays, two goes, two stays, two goes, etc. After installing the replacement chunks, you would just repeat the pattern for the remaining split chunks.
Isherwood has some great advice on exploring the full scope of issues that you may be facing. I would also look for any splitting of the rafters. At the ends isn't terribly offensive, but splitting away from the ends is more interesting (the worst case split all the way through at midspan will cost a rafter 75% of its stiffness and probably something like 40% of its strength).
