Much depends on wave size. A sudden strong wind will kick up small white caps on a short reach. Not much to worry about. Give the wind 10 km or so of water to run over and it doesn't much wind to kick up large waves.
Canoes generally are loaded stern heavy. If you travel downwind, you can get to the point where waves are breaking around the steersman. The bow weathervanes downwind, and is very difficult to point to a quartering run to shore. If you are going to paddle on windy waters, learn to trim your canoe to make it more controllable in wind.
When going into the wind there is a size of wave where the bow is in the crest, the middle is in the trough, and and the bow can't rise fast enough to keep water from coming in over the bow. This is why you often will quarter (meet the waves at a 30 to 60 degree angle) This is often a useful technique in haystacks on rapids.
Having waves directly on your beam is very unsettling, and requires practice, and a really solid low brace.
The hazard also depends on how heavily loaded you are. Bill Mason in one of his films is out on one of the great lakes playing in the surf. But it's an empty canoe, and he's better than most of us. Anyway, a lightly loaded canoe rises to the waves faster. Day tripping vs weekend trip vs month long expedition will give very different results.
Generally even with a couple weeks stuff, on small lakes, the being able to control your canoe in the wind is a more serious problem than the white caps are.
I used to work with a school that sent voyageur style canoes (21-26 feet long 6-9 people per canoe) all over Canada. These canoes are more heavily laden than tandem canoes are, drawing 6-9 inches of water and having about a foot of freeboard in the middle.
Our group's safety manual specified:
- With significant whitecaps, travel was to be within 1/2 km from shore. (Option to get to shore quickly if conditions got worse)
- If the wind was blowing off shore, travel was to be closer to the shore than the whitecaps. (Off shore winds can push you further off shore to where both wind and waves are much larger)
- In the event of a squall or sudden wind, head to shore, quartering if wave size warranted.
- An experienced (senior) staff member acts as sweep, watching for trouble, and making sure everyone gets to shore.
We traveled on some serious water: Superior, Reindeer, Wollaston, Athabasca, Great Slave, as well as many lakes that were "only" large enough to not have a visible far shore.
Mountain lakes are even more dangerous, as you can see less sky, and the winds are far less constant. I have been on Lake Abraham (N. Saskatchewan River) and have had winds go from 30 kph headwinds to calm to the same speed as a tailwind in the space of minutes. Going into the wind we were confident. Shore was close, and you could see the waves break. Once it became tail wind, we went to shore and waited it out.