You can definitely do this without a tour. My friend and I took a little picnic with us...and a blanket to sit on for the upper falls...and enjoyed a lovely snack at the "summit" of our hike.
The road is safe - make sure you have snow tires and that the weather has been clear for a couple of days - it is not the primary highway and so not a priority in getting ploughed. If you want to avoid driving a good portion of it, you can take the main Highway to Castle Junction and then take the road there to the Bow Valley Parkway it will bring you to just a Km or so from the Johnston's Canyon Parking lot.
I recommend "cleats" you can get a pair any "sports" shop...or even at the Dollar store - you can get something to give you a grip on the ice.
The hike is easy to moderate. The ice build up on the path depending on weather can be significant. We hiked when there was a lot of ice without the cleats and there were steeper areas where we had to sit down to stop ourselves from falling hard.
This is a truly amazing hike - both in Winter and in summer. And each for different reasons. In winter the ice cascades are spectacular. You may even see some Ice Climbers in certain areas. And even if it is snowing it gives you some amazing photos. In fact for picture taking a more cloudy day is better to reduce the stark contrast of light and shade.
You will love it.