When hiking or trekking in Iceland you need to cross rivers quite often. Some are small and clear but others are powerful and more difficult to cross. Only cross a river if you‘re 100% sure how to do it, feel good about it and are sure that you‘ll get to the other side safely. Talk to rangers and hut wardens in the area for information if the rivers are possible to cross or not. Special wading shoes are better than crossing barefoot.
Rivers often have lower water levels in the morning. Look around for a suitable location to cross. Be aware that where jeeps cross is not always good for crossing on foot. Narrow parts of the river are usually deeper than where it spreads, plus the spreading makes the current less strong.
Loosen all straps on backpacks and be sure not the have anything tied tight that could complicate things if you or anyone else might fall. Preferably wade the river with two or three other people at a time by clasping arms together at the elbows.