Lots of great questions, but they cover a lot of territory. I'll cover them as best as I can, and I'll point you to the best sources I know at the end. Sorry it's broken into two posts. Please put any comments or questions after the second so we can keep the thread a bit organized.

Were there typically professional soldiers in service to a realm or its ruler?

'Professional' is a bit of a loaded term. Were there guys who were probably veterans and expected to go to war each and every year? Absolutely. Did they prepare for fighting and were they better with a spear or sword than Joe-off-the-street? Almost certainly. But did they undergo any regulated, certified kind of boot-camp training? No, no evidence for that at all.

How were conscripts called to arms and how did they get to the battles? Would a farmer in Aquitaine have been expected to walk to the Saxon front?

'Conscript' is also something of a modern idea, and although there were medieval levies, they shouldn't be confused with conscription or the draft, which don't really appear until the Napoleonic period in the 1790s. If you were a lowly peon going to war, it's because you had a certain kind of relationship with a landowner or some other sort of patron, and you knew he'd take you to war with him. Your landlord had an agreement with his higher-up, or most likely with someone in the court or even the king himself, about how many people he would show up with and how they would be armed. So you had a personal relationship with your lord, and it would be his responsibility for arranging your transport to the campaign. For many folks, this probably meant a long trip on foot, but maybe you'd get an ox-cart to help carry your gear and provisions along the march.

Were conscripts generally paid, or just outfitted and maintained?

Again, this is probably a personal relationship with a lord or landowner. These are all unique arrangements, rarely written down, and probably based on some idea of what your dad did or, if you got the land as a gift, what the guy who worked there before you had to do.

Were formal declarations of war issued prior to deployment and/or engagement?

This is a really modern concept, which post-dates 1776 and the American Declaration of Independence. The idea that you can't have a legitimate international policy unless other nations acknowledge it as legitimate is actually pretty weird. Medieval lordship was based on what you could or couldn't actually do, not on what other lords might think you should ethically do. There was no need to declare war. If you could do it, you'd show up with swords on your neighbors doorsteps, and if you couldn't, then there was no use talking about it.

How were armies maintained during active aggressive campaigns?

Probably a lot of pillaging. There weren't many writers interested in talking about logistics, which might lead us to assume that logistical planning wasn't considered terribly important. Although we shouldn't be naive in that assumption, I still think it's most likely that logistics were improvised based on what you could find, and any logistical planning for invasions was in the form of emergency rations and having a place to fall back on if your raiding party went awry.

What constituted a single campaign from contemporary perspectives?

A summer season. The muster would happen in spring, and the king would be able to see who did or didn't show. Then he would know whether he needed to tamp down on things at home, or if he had enough strength to go abroad, and if he did, what caliber of enemy he could challenge. Then he'd float the idea, probably through backroom channels, and once he'd achieved sufficient consent to his plan, off he'd go into Saxony or Septimania, or what have you.

Was there a general notion of operational objective? E.g., did Charlemagne enter Saxony with a notion of war goals and targets, or did he just want to occupy as many structures and claim as much land as possible?

We don't know what Charlemagne wanted during the first ten years of the Saxon Wars—the sources don't say. Then, in 782, they start referring to the Saxons as rebels. This implies that, after ten years of large scale raids for plunder and prestige, Charlemagne had finally settled on gaining some sort of territorial authority over Saxony. A few laws followed, which really pushed priests and churches as the representatives of Carolingian government (keeping in mind that the separation of church and state wouldn't have made sense to a dynastic ruler who might appoint sons or nephews as bishops and abbots). So by the mid 780s, there seems to have been some notion of implementing territorial control over the broad region, and there was definitely an interest in reaping people and plunder from the campaigns, but I haven't seen anything to suggest that Charlemagne was actually eking out his own plots of land or trying to micro-manage the region.

Did contemporary commanders think in terms of self-contained "wars", encompassing certain battles and occupations, or was there just a "state of war" against a particular enemy?

It's hard to have a state of war without having a declared enemy. There were people you couldn't trust, and the Carolingians definitely thought of the Saxons as perfidious oath-breakers, but that didn't mean you were bound to go to war with the Saxons on any given year. If you showed up at the muster and it turned out that Charlemagne had other things on his mind, you could just go home without thinking about it terms of some national strategy against the Saxons. Of course, too many seasons without campaigning, and you might start to doubt Charlemagne's leadership or his abilities to profit you with the plunder of a successful campaign, so maybe picking on the usual suspects would be good for everyone, whether or not you thought that invading Saxony yet again would be particularly 'just'.

What happened (to the war, the army, and/or the individual soldier) if winter set in before a major military objective was obtained in Northern Europe?

You'd probably go home. And if the campaign wasn't going well late in the season, you'd probably leave early. I think a lot of the lower nobility owed more allegiance to their dependents who accompanied them to war than to their royal or lordly patrons who asked them to show up with their followers. After all, if a patron doesn't give you the benefit of a quick and profitable campaign, then they've failed their side of the bargain for being a capable patron. No use making matters worse by being a bad patron for your own soldiers.

How were armies typically organized?

That's really tough. It seems like a lot of prestige was attached to just showing up and whacking at each other, which meant that war was more about getting more guys to show up for the whacking then about making the strategic decisions to make the whacking more subtle or efficient. Reenactors can probably tell you a good deal about what you would need to prioritize to be most effective, but if they're judging efficiency based on how many 'kills' you can make with a foam sword rather than how many dependents you'll have left to till your fields and show up for the next year's levy, then their tactical experience might not mesh with historical priorities.

How was command distributed and assigned?

Prestige. Since I'm answering so many questions, I won't pause to look up the details, but at least once, two somewhat subordinate leaders decided to take their troops into battle without waiting for reinforcements led by a member of the royal family, since they wouldn't gain any prestige if they fought when he was there. They lost, and the chroniclers really beat them up for this, but then again, the chroniclers represented the view of the royal court, so that's to be expected. If they had won, they would have become more powerful regional lords with perhaps the potential to challenge the king himself. So military organization was about loyalty and prestige, expectations and aspirations, rather than some set form of rank structure or rationalized command and control.

How much large scale planning was there and how was it conducted?

If you've ever tried to do a group project with two people, it can take a lot of planning, finagling, and tying up of loose ends. Multiply this by several thousand, and you'll see the problems Charlemagne faced. He needed to develop a core staff of leaders small enough that he could effectively communicate and control with them, and he needed to cultivate their own leadership abilities without encouraging them to usurp his powers. And this core staff needed to do the same, all the way down the line to the lowliest aristocrat who showed up with nothing more than a horse and a slave to attend on him. Maybe they weren't planning long wagon trains or precise train schedules, but navigating these personal relationships and assessing all the ranked tiers of leadership and then managing them in the field took an almost miraculous amount of planning and deliberate conduct.