I studied music composition for a while in college, but never graduated with that degree... and we didn't study history of composition specifically... But he's my best answer since you don't have one yet.

Composers usually compose a piece using a simple instrument first... 95% of the time piano these days (or a straight up computer based composition system) but could have been harpsichord or something else long ago... Then they break up the melodies, etc to various parts of the orchestra. They certainly might have an instrument in mind for a melody or counterpoint while they are writing, but the basic approach is to serve the piece first.

That process of breaking it up is known as orchestration. That process often was and still is done by someone other than the composer. Some composers can and did do their own orchestrations, but it's very common for an assistant to do that with the supervision of the composer.

I will also day that for me personally, after I would write a piece I would sometimes have someone who played an instrument I wasn't as familiar with look over a part to make sure I wasn't asking them to do anything impossible on that instrument (or anything impossible for a player of average abilities).

But an orchestra isn't like a rock band where you want to make sure everyone has something to do and ask them to fill in a part. If there isn't something for a certain instrument for a while they just get a massive set of rests to count. That I can attest to because I was usually a tympanist when I played in orchestras. I can count rests like you wouldn't believe.

What you describe is a practice of a completely different musical tradition.

A composer from that period would play a couple instruments, but if he did not know how to actually play some others, he would certainly know what those instruments can do and what is the normal way to write things for them. Beethoven would not need help with that, but he did some times ask other musicians for help. He asked them to take a look at what he wrote to provide good fingerings, and to assess if some part was not too easy or difficult. He would ask top notch musicians, famous for their skills (that might have affected how difficult some sections are).

Some times these musicians had unfavourable opinions about his music. I am not talking about if some silly part is playable, but about aesthetic judgement. They would tell him he was insane, that the music was dense, nonsensical, and unplayable... Beethoven was not fazed by their remarks.

Some times he would use thematic material from other composers. That was very, very normal. I would not call that collaborative composition.

Some composers would ask others for their opinions on their music. This was common among friends, and people also tried to get input from the top composers. I would not call this collaborative composition, either. It is very different from people jamming together to produce a song.

As /u/pwnicholson mentioned, some times composers would not orchestrate themselves the music. Musicians had some times students/apprentices, and to save time they could ask them to orchestrate things following their instructions. As far as I know Beethoven did not do this for his symphonies. I would not call that specific form collaboration. There are cases in which somebody wrote some music, and some time later another musician would orchestrate it, or even re-orchestrate it. For that case there can be an interesting philosophical debate about whose composition that is (it can get kind of complicated to get into that, because you suddenly find yourself arguing about the definition and/or the nature of the music, the composer, the performer, the performance, and so on).

There are some cases in which composers decide to work together. One of the most cases is relevant to Beethoven.

Anton Diabelli was a music editor/publisher (and a composer). As a promotional idea, he wanted to publish a book of variations on a (silly) waltz. He asked many important composers to collaborate for the project. Fifty-one responded, including Beethoven. Now, Beethoven didn't just send a couple of cute variations for the book, and he wasn't too concerned about "blending in" with the guys. He wrote a complete set of thirty three variations, and that set is to this day one of the most significant ones in the piano repertoire. See, Beethoven didn't use to fuck around, and the damn thing lasts about an hour!!! I would not say he was actually "collaborating," but other musicians were.

I remember another famous case of an attempt at collaboration. When Rossini died in 1868, Giuseppe Verdi commissioned some composers to write sections for a requiem mass. It was meant to be a collective tribute to one of the greatest opera composers ever. Verdi wrote a massive section, and apparently the others all did their parts. The work was not premiered in their lifetimes. Verdi took the part he had written, and later wrote a whole massive requiem all by himself. It's a great work, of the kind for which you should seriously get good headphones or a nice sound system and turn the volume up. It has everything, from the bad ass section you can blast in your car while driving, to the super dramatic part you play while flaying people in the basement cooking a fancy dinner and sipping wine.

These stories might give you the impression that classical composers do not work well together, and I guess you would not be wrong. This kind of music has been very individualistic, and there were (and are) a lot of hierarchies in the day to day life of musicians of the classical world.

There were cases in which composers actually worked together, see this list.

Now, there's one special form of collaboration. Baroque and earlier music were full of improvisation, the composer work was to create a foundation on which to build. I guess we could argue there is some form of collaboration in that, but different from the one your question is about.