Our first advice is that you take your time to visit Hengifoss. There is so much more to explore in the surroundings then just that waterfalls. You can learn about that on this website and use it to help planning your trip.
Hiking in summer
The high season (July) it can be crowded by Hengifoss but it is mainly just jammed with cars at the parking lot. If you don't find a space to park you can just continue further into the valley and check the visitor's center for Vatnajökull National Park at Skriðuklaustur (5km) and then get back and see if some have moved.
The waterfall and the big gorge is facing southeast so if you want to have the sun on the falls you need to go there in the morning. In June and July there is usually plenty of water in the river to make Hengifoss magnificent but in August if the summer er really dry you may expect the falls to be not so broad, but is certainly is still enormously high.
Late May and early June can be risky because of melting snow in the highlands, causing high levels of water in creeks and rivers. You can expect muddy trails and slippery paths on you way to the waterfall and the need to wade some small streams. By autumn the rain can make the trails muddy as well but usually you will not have to wade any streams unless you want to enter the gorge and go close up to the base of the great waterfall.
Hiking in winter
There are more and more people that go to Hengifoss in wintertime. But then you need to be extremely cautious. The trails and paths get icy and very slippery so stay away from the edge of the canyon and be aware of the danger. It is not save to enter the gorge by the big falls in winter, due to a risk of falling ice from the cliffs.
There are nearby companies that offer you a guided tour to Hengifoss in wintertime just as in the summer. We can recommend wildboys.is to take care of your winter hike.