Dust- the higher the intake the less dust. Laws of physics prevail. Dust is heavier than air so it falls to the ground. Therefore there will be less particles the further you get off the ground.
But you're going to have a filter, regardless of which setup you use. The question is: if you leave the air intake box stock, will there be enough dust clogging up the filter that you'll have to change out the filter sooner than if you'd use raised air intake?
For most overlanders doing a few weekend trips, if that, per month, I'd argue no. Maybe there are exceptions to some people who are constantly driving dirt roads out west, but if I were a weekend warrior in Maryland, I don't think I'd be seeing enough dust to warrant a snorkel.
Temperature: the air is a lot cooler further off the ground. People go to a lot of trouble to install cold air intakes etc when the answer is just supply the air from a cooler spot to start with. This cooler air partially or completely offsets the next item.
I think most modern air intake systems are well designed and I don't see an aftermarket snorkel providing a noticeable difference in air temperature versus a factory design, especially compared to the more advanced factory units that can modify the intake route depending on the air quality. A raised air intake is, at most, 4-5 ft higher than a stock intake; I don't see that 4-5 ft height advantage allowing for much, if any, difference in intake air temp's.
Loss of power: yes there is more air flow restriction using a snorkel. This is especially so using a cyclonic head over a ram head. But if you follow this rabbit right down it's hole we can get into the facts that you can flow a lot more air with no filter or a more open filter (K&N). Obviously this puts you more at risk of dusting an engine. You are the only one that can determine the the level of restriction you are prepared to bear with the downside being a reduction in power. Personally don't drive on a dyno so pure peak power/performance figures are irrelevant. As long as it still flows enough and you are not trying to suck a marble through a water hose then things should be fine.
Okay, but the filters being equal, a raised air intake creates more inefficiencies versus a factory intake system. I don't know how much of a difference can be noticed by the butt dyno, but the OEM provided HP/Torque and towing ratings because of how certain systems, to include the air intake, were designed. It might be a difference that is barely noticeable, but it is something people should be aware of before purchasing an aftermarket intake.
Water crossings: where I came from in Australia water crossing were not much of an issue 99% of the time so that was not why we had snorkels. But when it flooded out there the water covered everything for miles. We always tried to keep the water level below the top of the tires. But sometimes there are oops moments. So it really was a nice benefit but not a decision point.
I understand the theory behind raised air intakes and water crossings. I think the reality for most modern vehicles is that hood-high water levels will be frying their electronics, so a flooded engine will be the least of their worries.
Most modern gasoline vehicles will fry the electronics if they encounter water depths of the video a few posts back. Older mechanical diesels not relying on complex circuit boards can run as long as they get air and the fuel doesn't get contaminated.
^This.