The frontiersman had to have affordable tools he could rely on. He really wasn't that much different than we are in this respect, but his reliance on his tools wasn't an inconvenience. It was life threatening if his tools failed him.
Iron wasn't easily obtained, so any items made of iron would be used used until they were worn out, then the iron made into another useful tool, implement, or piece of hardware.
The typical frontier settler would bring an iron headed axe of some design with him, and usually that was his major investment in iron tools. Rakes, shovels and most other implements would be made of wood. One other item of iron that most would bring was a plowshare. Plowshares of wood were used by many, but wore out quickly in the often rocky soil, and an iron share would last for years.
If he were a lucky or of better means, he may be able to afford both a felling axe and a broad axe. The felling axe is what he would use to cut down trees, and the broad axe is what he would use to shape them into materials for construction.
Many other tools such as drawknives, hatchets, spoon bits (for drilling holes), chisels, files would be invaluable, but not every frontiersman had these items available to him.
The frontiersman would depend on knives and belt axes for most of his personal needs. He could take his knife and make many of the things he required for both subsistence and comfort. The belt axe would provide materials for his whittling, firewood, and saplings to build his camp when away from home. They would both be used as weapons when needed, and were as important to survival as his firelock.
Most often, the knife that a man would carry was a rather simple knife, similar to what we would consider a butcher knife. Frequently, he carried whatever he could get from the family cooking implements.
Trade knives were quite common, and although not exceptional in beauty, they were sturdy, reliable, and well made knives.
One other item that was carried by many of the woodsmen was a belt axe. These varied from simple trade axes to beautifully made and decorated pieces of art. The one shown above is a double-eared, hammer poled rifleman's axe. The exact design of the axe would vary with local availability.