I think a three day walkout is totally, totally unrealistic. And I have done 30+ km daily for days at a stretch with heavy gear in bad weather.
If you are not on a trail, unsure of where you are going, and cold and hungry, I think it's much more realistic to figure on 5 km a day and hope to be pleasantly surprised.
In the event of a major snowfall that could be cut down to 1 km a day, no joke. I am bigger and stronger than most people and I do heavy physical work day in and day out, and I have a lot of experience in major trekking expeditions, and I have had 1 km days in heavy snow.
Anyway there are two ways to go for a knife in this kind of situation - a big chopper to replace the obviously more effective axe, or a slicer and hope that good slicing ability is enough to let you get away without chopping anything.
I would be pretty annoyed to be without an axe in this situation, but without an axe, I could go either way on chopper/slicer. A big chopper of any sort would be good in some ways, and a smaller 4" slicer could do you a lot of good as well.
Right now I wouldn't expect severe cold, so I would be thinking small fires would probably do you, making the sacrifices you make to get a good chopping knife probably not worthwhile. If it's only five or ten below big fires are not TOO necessary - although at those temps I find the weather is often much windier, so it could be a bit of a toss up.
Still, I think I would lean towards a slicing knife.
I'd say it depends. This isn't exactly Antarctica, and it's autumn, not midwinter, so it's pretty unlikely that there will be 100+ cm of soft snow around. I've lived in rather cold conditions all my life, and yet I have never, not ever, seen such weather that I could only move 1 km a day. And I've had to go without skiis or snowshoes in sub -25 C weather with over 100 cm of snow, carrying fairly heavy gear. Very high up in the mountains, sure, it could be less than 1 km, even, but in a forest... if trees can live there, I can walk there. A forest during autumn? Unless someone has shot me, there's no way I'll total less than 10 km a day, assuming I have even the faintest idea where I'm going, and that the trees aren't growing from the bottom of a lake.
It depends on the weather and what you have, and who you are. I'm not bigger than most people, which, to me, is good, since I'm not as heavy. Assuming I'm carrying equipment only for myself, and I don't have a heavy as hell assault rifle and ammunition with me, it's going to be a pretty light-footed journey. And in this case, if I don't have anything beyond a knife and clothes, it's going to be about as easy as it can possibly get, with no extra weight. But as I said, I'd rather have the compass than a knife - even lighter, and then I'd certainly always know where I'm going. Nothing slows a man down quite like constantly checking for the right direction with the most primitive of means, and nobody wants to go in circles. I've always liked running, so that helps quite a lot in terms of physical stamina. In the woods, stamina is much more important than raw strength. It's not how much one can lift, but how long one can walk, tired and without food. The most I have gone without eating anything was, I believe, four days, and it wasn't half bad. Felt like being on a diet, but certainly didn't stop me from running or walking pretty much normal distances. I admit I wouldn't have been able to beat any of my weightlifting records (which aren't anything to brag about anyway, certainly not to anyone who has seriously trained in that sport), though. As long as there's drinking water, lack of food isn't very bad, not for periods less than a week for a person used to not eating four large meals a day. And since there are lakes, there is water.
The main reason I'll still say this could be walked out of in 3 days is the clothes - if you've got the proper clothes for the weather (and proper means proper, and proper means being prepared for weather more severe than the current, within reasonable extent), there's not much need for a fire, at least not if you're used to colder climates.
I think you'd do just fine with only a slicer knife, as long as we're not building a cabin. I'd want an axe, too, if I knew I was being dropped off into real middle of nowhere, like some places in Siberia or the more remote parts of Canada. But this isn't that bad at all. Of course, for the city folk, anything beyond 1 km from the nearest population center is in the middle of nowhere.
