Is a cooldown really necessary after a speed session if weights are going to be done directly afterwards?

go straight to the weights after track.the whole emphasis is to keep warm and loose from one to the other

Should a cooldown be done after weights?

I would say that warm-downs are very minor after power and strength training since most training sessions will have very little byproducts. Just finding parking at certain tracks (inside joke) can be the warm-down. In fact, if you are doing a weight session after the speed work take advantage of the heat and activation state, since you save re-warming up.

RE: parking at certain tracks
I find that’s true of most tracks, considering that most of them are at universities, which are not exactly known for abundant, convenient parking, especially for non-students (no permit).

For high intensity days, the best post-workout activity is relaxing the muscles (stretching, light massage, etc.). Like Clemson mentioned, there’s not a lot of metabolic byproducts from that kind of work.

I guess I’m pretty lucky for now. At my high school track you’ll be lucky to find 1 car in the parking lot! Of course to actually get onto the track I have jump over a 6ft fence, then climb over a 15ft tall fence then hop a 4ft tall fence! No word on when the barb wire or guard dogs will be added. Would this be considered high-intensity exercise?