I think rucking might be a good replacement. Walking while carrying weight is a thing humans were meant to do. Jogging and running are good too of course no debate there. But it's surprisingly easy to injure yourself running jogging. Rucking I think has maybe equal benefit, less downside. 

 Low impact jogging = injury prevention.

People have it twisted because they push themselves improperly. 

 This is true 

 I use to run a lot. Small kids + long winter. Easier to stay consistent with the spinning bike. Other than that I walk a lot 

 Winter = the best jogging experience.

All the benefits of running & cold exposure. 

 I used to do that a lot too. Lots of dark ice. Phone would eventually give out: the battery didn’t do well with weather that cold. 
Also urban area. Sidewalks is not the best for the joints (concrete). Street (asphalt) is better but too much cars 

 Yes I agree, I never jog on concrete - only natural surfaces.