Grumbler: that (the) last winter was very cold and they had HAD to feed the animals. (After SAID you have to use the past perfect to express the simple past, because the present perfect refers to now).

(Speaking in the present) - [mother]: Where's your brother? It's time for dinner. [son]: The French club is having a party tonight and he HAD to stay late. (Speaking about last summer) - [mother]: Why didn't your school organize a trip to Europe last summer? [son]: I asked the teacher and he SAID that there had been too many bombings and they HAD HAD to cancel the trip.

Here's another example: https://www.lingvolive.com/en-us/community/posts/1116593

Corrected, thank you.
However, I still don't understand why this applies to "they had ", but doesn't apply to "winter was". Both seem to be identical in terms of the time and continuity. They had to feed animals regularly, not once.

Actually, you can say Last winter HAD BEEN very cold, which actually sounds better to me, but for some reason WAS doesn't bother me in that part.