Yes. There would often be two horns and two trumpets. Trombones were added in the late Classical period. The tuba wasn't invented until the 1840s, well into the Romantic era.
acoustically
String Instruments
The actual count and type of woodwinds instruments required in an orchestra is determined by the composer of the piece. Not every single woodwind instrument is used in every single classical piece.
The orchestra saw a complete upheaval in the Classical period. Here are what I think would be the three most important: Firstly, conductors got off their harpsichords and began conducting in the modern style with a stick. Before that, they simply outlined the tune and held the timing together with a continuo. Next, the instrumentation changed. Recorders fell out of use, being replaced by the modern transverse flute. Clarinets were also first introduced to the orchestra in this time. Finally, the locations and sizes of orchestra began to change. They moved out of courts and private locations where they were restricted in size and grew into much larger orchestras, suited for opera houses and concert halls.
It all depends on the orchestra and what piece they are playing. You will see the use of many different traditional and non-traditional instruments in the modern orchestra. In the classical orchestra it would be uncommon to see a trombone.
acoustically
String Instruments
Most of the instruments used in classical music are instruments used in an orchestra such as violin, flute, cello and double bass. Pianos and organ are also examples of such instruments.
The actual count and type of woodwinds instruments required in an orchestra is determined by the composer of the piece. Not every single woodwind instrument is used in every single classical piece.
The orchestra saw a complete upheaval in the Classical period. Here are what I think would be the three most important: Firstly, conductors got off their harpsichords and began conducting in the modern style with a stick. Before that, they simply outlined the tune and held the timing together with a continuo. Next, the instrumentation changed. Recorders fell out of use, being replaced by the modern transverse flute. Clarinets were also first introduced to the orchestra in this time. Finally, the locations and sizes of orchestra began to change. They moved out of courts and private locations where they were restricted in size and grew into much larger orchestras, suited for opera houses and concert halls.
Most brass instruments, like the trombone and trumpet, are used in orchestras (think The Imperial March from Star Wars). They are very influential in orchestra music and are used when majestic sounding or scary loud parts are needed. The brass instruments are not often used in chamber orchestra, as they are too LOUD! Trumpets are also used in popular music, particularly jazz, where they will often fill in with a few rhymic chords at the end of a line while the singer takes a breath (a good example is 'Let's Face the Music' by Nat King Cole - the trumpets sound a bit funny because they are muted - they have a hollow lump of metal inside the bell, where the sound comes out). Also, in the UK an old tradition that is dying out is one for Brass Bands. These are formed of brass instruments and percussion. The film Brassed Off is about a Brass Band, and the most famous piece of Brass Band music is probably the Floral Dance. Brass instruments are used in almost all kinds of music. There have been brass instruments in rock groups, are used in all types of jazz and all types of classical pieces. If you are looking for some great brass players try Louis Armstrong, Miles Davis and Freddie Hubbards for a start, and those are just the trumpets! There are many classical movements and composers who've used brass, you've just got to listen for the special timbre of the instrument.
Trumpet
It all depends on the orchestra and what piece they are playing. You will see the use of many different traditional and non-traditional instruments in the modern orchestra. In the classical orchestra it would be uncommon to see a trombone.
The tuba is the biggest brass instrument used in a symphony orchestra. (There are some very rare special pieces of music where a composer might call for an instrument that is not normally in an orchestra. For example, there is a family of brass instruments called ophicleides that were used in the 1800's, and those came in many sizes, including ones as big as the tuba.)
in a string orchestra the instruments are: Bass Violin Viola Cello.
The french horn is a brass instrument. The sound of the horn can mix very nice with the sound of woodwind instruments. The horn is the only brass instrument that is used in the classical wind quintet, which consist of flute, oboe, clarinet, bassoon and horn. This quintet is sometimes referred to as "woodwind quintet", although the horn really is not a woodwind.
Brass instruments, like most instruments, can be used for almost anything! They are most commonly used for bands and orchestras though. Trumpets and bugles, both types of brass instruments, also have a long histories of use in the military. Today, brass instruments are often taught in school bands, and can be used to teach the foundations of music!