Yes you can feel the difference in steering response and available traction.
Bog down? Some surfaces will have better traction than others but "bog down" probably does not apply to winter tires in any conditions. You will have less traction in dry or wet compared to summer tires in 40-50 F and up. It means more wheel spin.
It also means that in wet you may have much less traction than before.
You will have more fun in "going around turns" as there will be less available traction if your fun is similar to my fun definition.
Define "accelerating like normal".
There are different types of winter tires. Winter performance tires are similar to all seasons in wet/dry performance.
16" winter set up has more sidewall to deal with unseen/unavoidable obstacles like potholes.