.
I'm in the southeast - surface water freezing is usually only a few days per year (if that), so I can't comment on the freezing issues.
If you have heavy traffic loading (emphasis on weight much more than cycles), then the cover might be a concern. In the situation you described, 12 inches should be more than enough. (You could probably drive a loaded pickup over that in decent soils and not have a problem - depending on the pipe, bed and backfill construction method/care).
I rarely see these small pipes and low-head inlets work well - often failing within a year after installation - but it does depend on the watershed. The problem I see is inlet/pipe clogging. If this system is in an "ultra-urban" area (near 100% paved/impervious surface) with no trash, debris, or sediment, then the system might work okay.
I don't use anything less than a 15" diameter pipe for stormwater conveyance and only that if all inlets have fully grated covers. Otherwise, 18" diameter is the minimum I use. The one exception to this is roof drains - to which I might connect 8" or 12" diameter pipes. Have you checked out other installations in similar areas to assess how well those are functioning? This is not about the clean water hydraulics - this is about the clogging. The hydraulic analysis may very well show that everything is fine with a 4" diamater pipe, but that is not reality in most cases - larger pipes are needed to address clogging. The 4" diamater might might need to be an 18" diameter pipe to prevent clogging failure.
Connecting just below the grate should be no problem physically, but the resultant low forcing head at the inlet would likely be a problem.
.
tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation