It's legal here to walk a dog while cycling.
It's great for the dog too, as they get to go a little faster than a human's walking pace, which is like a snail's pace for a large dog.
Most of all, though, it's pleasant for people as they feel happy enough to do it.
The law seems to think that more than one dog would be difficult to control while cycling. Only one dog at a time is legal. However, I've seen people ride right through the very centre of cities here with two dogs on leads.
It's not just dogs that get to have this fun. The photo on the right shows someone leading a horse.
There's a different attitude to safety on bikes here, brought about by a much higher level of safety for cyclists than in most parts of the world. Both of these photos were taken on the cycle paths which are a large part of the reason for the very high subjective and actual safety.
There are no helmets, no fluorescent clothing, no vehicular cycling. Riding a bike here is safe without those reactions to a hostile environment. I'm not mocking those who adhere to such things presently. They can make sense in context. Back when I lived in the UK I also did all of these at different (or sometimes the same) times. I also used to think it wasn't a good idea to lead a dog by bike...
A later blog post includes a video of walking harry by bike.
We sell some solutions for carrying dogs by bicycle
The first photo is of me with our dog, Harry. He also appears on youtube. Another way to transport a dog is in a bike basket. I also have a later post including a video of cycling with Harry.