Having spent my early years on keyboard, there's the tendency to think of a series of notes as mere switches to be flipped in sequence, but on the horn, more than any other instrument I've ever played, every phrase is more sculptural as it moves from one note to the next, with every note's tone and intensity affecting the next and so on down the line.This is a very useful realisation. This "sculpting" of notes is not merely something which happens from one note to the next, but you can also change the character of a note during an individual note of any significant length.
You can think of the tempo (including rubatos), tone, volume, pitch and attack as five entirely independent variables which you can can adjust in order to get the musical effect you want.
The number of possible permutations you can choose from is huge. Music notation only gives you the merest clue as to the appropriate combination in any particular circumstance. The rest you have to work out for yourself.
So how do you decide what is the right thing to do?
The first thing is to realise that you actually have a choice. The second is to acquire sufficient technical control over the different aspects of playing that you can vary all these things independently at need. I've described before how to control tone and volume independently of each other, which are probably the hardest two items to separate.
Once you have the technical control, you then need to understand how to use it musically. It's quite hard to describe in words how to do this.
The dots on the page give you the pitch and a general idea about tempo, volume and attack. There may be indications that rubato is appropriate. Notes may have slurs, tenuto marks, accents, staccato dots etc. Very occasionally you'll get some kind of instruction about tone, e.g. dolce or cantabile. But with staccato for instance, you have a considerable choice as to how short you make the staccato and how much of an attack you put into it. With crescendos and diminuendos, you can decide how far you will change the volume, and you can also vary the rate of change of volume during a crescendo. On a long crescendo, I'll quite often save up most of the change of volume for the last bar or two. The notes are just a general description, it is your job to turn them into music.
There is a lot of tradition involved in this. When you are a student, this is one of the concepts your teacher should be introducing, whether or not you realise it at the time. In your early years playing, you sit next to people who have been doing it for longer, you absorb how they do it and you mimic them, consciously or otherwise. Gradually you learn enough to be able to make your own decisions about this, so you aren't merely copying what you have been taught or shown. As a result, traditions change over time, as each new generation of players finds its own approach.
And you also have realise that if you are playing in a group, the sound you produce is part of a composite tone in combination with the other players. For instance the horn can used to warm up a cello tone such as in the opening of Dvorak's 8th Symphony. And there is an amazing moment in Mahler 9, where horns 1 & 2 play a note fortissomo diminuendo, and horns 3 & 4 play the same note piano crescendo, but handstopped. So the overall effect is of a more or less constant volume, but a gradual change in tone colour as the handstopped note takes over from the open. (It's four bars before figure 13 in the first movement, if you want to look it up.) So your choices about how to play any passage also have to be made in the context of what is going on around you.
But ultimately you are there with the mouthpiece to your lips and an audience in front of you, and only you who can decide how you will play the next phrase. Realise that you have a decision, and do your very best to make it sound musical.