@motherofakoalaboy - have you checked that his shoes fit properly? If they have become uncomfortable, that might explain his unwillingness to walk.
If his shoes are fine, then using a tricycle seems like the best idea - he will still be getting exercise, and won’t be being carried.
I also wonder about turning round and going home as soon as he starts tantrumming - very calmly say “Yes, daddy will carry you but we are going home, not to the park. If you want to go to the park, you need to walk or ride your tricycle.”
I remember so clearly how difficult it is to cope with the terrible twos - when my eldest was that age, I was in tears, on the phone to dh one morning, because ds1 had had a massive, hour long tantrum the night before and had already been screaming for nearly an hour, and it was barely nine am. While I was on the phone, the screaming stopped, so I hung up and went to find ds1 - he was standing by the kitchen bin, eating some left over tortilla chips we had thrown away the night before, and that was what had stopped his tantrum.
But that isn’t even the worst part - I looked at ds1 and I knew that, if I took away his delicious bin-snack, he would go straight into another tantrum, and I couldn’t face the prospect of more hours of screaming, so I let him carry on eating, until he’d had enough, and wandered off!!
I did then empty and hide the bin, so he couldn’t do it again, and he was completely fine - cast iron digestion - but it was not my finest parenting moment. He is now in his 30s, with three kids of his own, and we all survived the toddler tantrum years, so don’t worry - you will get through it too, I promise.