Positions - bow
The front (bow) hand holds the bow. The bow may be helt vertically, canted (in the 90 degrees range), or horizontally. You have exactly 90 degrees available for canting; any other angles are usable only scarcely, during some very awkward archery tricks.
You usually shoot from a bow held vertically, or a bit slanted (say maximally 45 degrees). It is possible to shoot from horizontal or almost horizontal bow, but it has its disadvantages.
Disadvantages
1) The bowstring is under the bow hand, so you cannot raise the bow in front of your eyes. Thus you can shoot only in a instinctive way. I am not quite sure in shooting like that, but certainly this can be trained.
2) It is not possible to draw the string as much as you can when holding the bow vertically, because you own body stays in the way.
3) In thicket the horizontal held bow is more likely to catch somewhere.
Advantages
However it must be said that with suitable bow (and circumstances) the horizontal shooting is very usable. Point 1) does not mean anything if you shoot instinctively, which is what most "natural" archers do and did. Point 2) is not problem if you shoot from a "short longbow" (short straight bow without recurve), which cannot be drawn more all the same. The same short bow, with also the kind of terrain you usually live in, together weaken even point 3). It all means that under certain conditions you don't meet any stated disadvantage, and horizontal shooting makes quite a good sense. Because it also has advantages:
1) On the horseback there is smaller chance to catch or hit your horse.
2) The ground does not stay in the way when shooting from kneeling, sitting, or very crouched position.
3) It fixes the arrow in place better, the arrow does not slant.
4) You can hide behind something better, because the bow does not tower above you. You can also better "hide" behind your bow.
Conclusion
With the bow that can be drawn to a full draw, you often hold the bow horizontally only when nocking the arrow, or when waiting with arrow nocked but string undrawn. During the shot itself you usually cant the bow nearer to the vertical position. The exception being situations when you need fast and totally instinctive shot to a small distance.
However with suitable bow (short one that cannot be drawn much), the horizontal position can be used much more intensively, and it also was in history. Horizontal bow was very often used for example by american plains indians (horseback shooting) or ancient Greek (shooting often crouched or rather half-kneeling).
