Winter tires on the trailer??

Hello our caravan just ready for winter camping! I am unsure if you should upgrade the caravan to winter tires. I heard some, which say is not necessary, because it only rolls behind. Towing vehicle with winter tires and snow chains is absolutely sufficient. A winter WoWa driver has even made extra tests on ice and snow times with summer tires and then with winter tires and has found no difference. A truck driver told me is unnecessary he drives on its 40 tonner only on the drive axle with winter tyres. More is not prescribed by the legislator since 1.05.06. What do you mean?? I actually wanted to buy winter tyres but in the original size 205/70 R14 there are no winter tyres and on 185 or 195/70 R14 I actually don’t want to drive because I think that the driving behavior will definitely become more spongey?! Or insecure greetings PP