I have three sizes of Granfors Bruks axes from the Mini to the Wildlife to the Small Forest Axe. Those forged Swedish axes will cut. For long foot travel, the lightest tool you can take means more comfort while afoot. If your style is close to the vehicle then take full sized tools all the time. Smaller axes are more accurate but bigger ones do eat wood much faster.
As far as fires, I like mine small too. I leave the front open and if it is cold I build up the back of the structure to reflect more heat. Oblong will allow you to burn some wood while cooking over coals at the other end.
Most of the time I never use an axe and break wood with hands or with feet but when using a small rock structure and wrist sized wood a small saw works best if the wood is tough. I like the Bahco Laplander. It cuts through wood fast. If it needs any splitting, a Mora and baton will do the job.
In the north woods, some place really cold with snow or in the very wet climates, a good axe will be cherished.
I have a Lee Reeves tomahawk that does not quite get it. My Granfors Bruks Mini blows it away and the Wildlife is a serious tool. If I really want a working axe, the Small Forest Axe sees the most use of all of them. It can be used one or two handed and the head has enough heft to do some real work and some real damage. The small saw is a much safer tool. It’s a lot lighter and more compact too.