Realistically, your biggest irritations while hiking are likely to be mosquitoes, flies and blackflies and hiking in the Canadian wilderness is far safer than wandering around most cities, but make no mistake, bears are potentially very dangerous, and most people blow a whistle while walking in bear country to warn them off. If confronted don’t run, make loud noises or sudden movements, all of which are likely to provoke an attack.
Cougars pose a somewhat lesser threat, with most attacks occurring in BC – unlike bears, the best strategy with cougars is to try and fight them off (they usually avoid groups altogether).
Snake bites are more common in some parts of Canada (there are rattlesnakes in Georgian Bay Islands National Park for example), but even then only a handful are reported each year and fatalities are rare – wear proper boots and if you do disturb a snake back away so that it has room to move freely. Even the most venomous bites can be treated successfully if you receive immediate medical attention (call t 911 or notify park staff).