I'm frequently tempted to solder to devices that are still powered. Assuming that:
Is it possible to damage anything (device, myself, soldering iron) by soldering things on the board without powering it off? Are there any hazards that I haven't considered?
Typically, no - if you're careful. You can use gas-powered iron or just unplug the usual one from its power source just prior to making a joint (that's what I do). It is actually quite convenient during debugging since you just resolder homemade probes from one test point to another instead of figuring out how to re-clip fancy expensive ones without shorting adjacent pins. For parts with 0.5 mm pitch and less soldering is the easiest way to attach a probe since you'd have to probe under a microscope anyway and while you move your eyes from the board to the display of your instrument you can also easily move a probe if you're holding it with your hand.
"Careful" is very important. No matter how good you think you are never solder live line-powered circuits, under any circumstances. At my job I don't have an iron in a room where I work with SMPS stuff.
Figure that while soldering you are likely to bump with your soldering iron anything which is too close to the things you are trying to solder. This is likely to momentarily short things. Further, some soldering irons are constructed to have a conductive path from their tip to ground; this may help avoid ESD hazards, but may sometimes pose a problem if that path interacts badly with the circuit being soldered.
In some cases, these issues don't pose any problem. In many cases, they pose a slight concern, but no real danger. For example, if an embedded system takes an annoying amount of time to boot up, and an accidental short would disrupt its operation in such fashion as to require a reboot but have no other consequence, one might decide to solder such a device while in operation even if there was a 25% chance of bumping something. Figure that if everything works cleanly, one has saved the hassle of rebooting, and if one slips up one still would hardly be any worse off than if the circuit had been powered down first.
Of course, there are also many common scenarios where a slip up could destroy the circuit being worked upon, and some where it could pose a safety risk to the person soldering, so it's important to use good judgment. Absent a really good reason, I would be inclined to solder on live circuits only when the consequences of an accidental short would be minimal.
If you use a regular soldering iron while the device is on, you could short out the pin/trace your soldering.
Even if you do use a hot air or gas soldering iron there are other problems:
One problem that you may encounter is exceeding the absolute maximum temperature of a given part, this especially applies when the part is on. If the part is off this doesn't matter as much because a part is able to handle the soldering temperature profile for that part. If you exceed the absolute maximum rating, damage is sure to occur.
When metals are hot AND have current flowing through them you can get bad things like electromigration that can damage an IC.
This can also happen if you turn off the device and solder a part, and don't let it cool sufficiently before turning the device back on. Don't exceed, maximum temperatures in the datasheet, and follow the temperature ramp for solder profiles on a package datasheet.
Actually I think there is a bigger problem in soldering while circuit connected to the power. This is completely based on my experiences, I learnt it in hard way (I damaged 3 MFRC522 boards in a row till I found out the cause). I think in soldering a board, there are at least 2 different kinds of metal(Cupper,Lead and Iron in soldering iron) together with intense heat, it makes an unintentional thermostat and it will produce some voltage (if you have an LED near the point you are soldering you may notice some blinks) in your circuit and based on point you are soldering this voltage may add to potential on that point even if it is negligible and exceeds the maximum voltage rating and damages your IC. I categorically recommend you to cut your board off the power before doing anything. cutting off means that you should even disconnect your ground connection
