Ericja, I think the telling criteria is what ground you are walking upon. Keep in mind that I'm answering you as an interesting thought experiment here, because I may be in a similar situation this summer (hiking + hunting). I'm no legal authority!
If it's permitted to hunt on the land you're walking on, you can obviously have the gun in your hands. if you can hold a gun, I don't see any possible argument against having it attached securely to your backpack. You will need a sock to wrap it into after sundown, though. And you can never, ever leave your pack unattended (better drag it in your tent at night, or you'll have armed racoons to deal with the next morning!).
If you're not on hunting lands, then the local bylaws are probably the key. There's usually restrictions concerning roads and hiking trails (I believe the trans-Canada trail in particular is a restricted area as far as weapons go, and the same thing mat apply to utilities rights-of-way). I suspect most municipalities and townships will be nervous if someone openly carries a weapon on public streets, roads and parks, even for the most innocent of purposes (such as hiking between two hunting areas). At best, you might get many free rides from nice police officers. At worse, they'll use whatever bylaw is handy to fine you and confiscate the weapon. You might placate them if the weapon is either disassembled and hidden in your bags (like those survival carbines that stores the action and barrel into their stock) or if there is a trigger lock installed on it at all time and it's covered by a gun sock.
Of course, the problem then is that when you do need your rifle, you got to ask the wildlife to take an appointment for 10 minutes later.
As far as transportation, the Firearm Act is somewhat limited in scope: the weapon has to be unloaded and the rest of the section is all about being leaving it in unattended vehicles. There's really no provisions for transporting a weapon either on foot or mounted.
TRANSPORTATION OF NON-RESTRICTED FIREARMS
10. (1) An individual may transport a non-restricted firearm only if
(a) except in the case of a muzzle-loading firearm that is being transported between hunting sites, it is unloaded; and
(b) in the case of a muzzle-loading firearm that is being transported between hunting sites, its firing cap or flint is removed.
(2) Subject to subsection (3), an individual may transport a non-restricted firearm in an
unattended vehicle only if
(a) when the vehicle is equipped with a trunk or similar compartment that can be securely locked, the non-restricted firearm is in that trunk or compartment and the trunk or compartment is securely locked; and
(b) when the vehicle is not equipped with a trunk or similar compartment that can be securely locked, the non-restricted firearm is not visible from outside the vehicle and the vehicle, or the part that contains the non-restricted firearm, is securely locked.
(3) If, in a remote wilderness area that is not subject to any visible or otherwise reasonably ascertainable use incompatible with hunting, an individual is transporting a non-restricted firearm in an
unattended vehicle that is not equipped with a trunk or similar compartment that can be securely locked, and the vehicle or the part of it that contains the non-restricted firearm cannot be securely locked, the individual shall ensure that the non-restricted firearm
(a) is not visible; and
(b) is rendered inoperable by a secure locking device, unless the individual reasonably requires the non-restricted firearm for the control of predators.
Concerning the hunting caliber, it looks like there's really no restrictions if you're on hunting-permitted lands except during the Sep to Dec period when the big game season is on. Then you can't have anything with more than 400 foot-pound of energy (say, 22LR) with you unless you also have a big game (deer and over) license. And you must wear nice orange clothes.
Given the space/weight considerations of a hiker, you might want to go for the lightest 22LR you can find or for a break-down weapon like the Ruger 10/22 takedown or one of the survival carbine. Personally, my only worry is that a 22 is fine for shooting a rabid chihuahua, perhaps not so fine if you're facing a rottweiler or a bear. For that, I'd prefer one of the 9mm carbines (Beretta CX4, JR Carbine, etc.) with hollow point ammo. If you can't stop a bear with 10 rounds of 9mm point blank, he was Superbear and you were doomed anyhow.