When you dream of a carriage it can have several meanings depending on the context you were dreaming of it about. If you were dreaming of a carriage carrying a baby then this dream might mean that you need to have a more responsible attitude toward children. The dream is trying to warn you that you need to learn to take care of children with a more caring attitude or you will end up causing harm to them. The carriage is there so that they can be safely placed in it and rocked to sleep. Dreaming of a carriage in this context can also have much more broad interpretations though.
For example, to dream of a carriage might also mean that you need to take a more relaxed view towards your own childhood. Lots of traumatic things can happen during our childhood years that end up going on to affect us into adulthood in negative ways, but what a dream about a carriage might be telling you is that you need to relax. A carriage is a way to get a baby to calm down, thus if you are dreaming about a carriage it could be a reaction resulting from trauma that you suffered during your childhood. This means that you need to lay all of those issues to rest and go on with your life as you were before. In essence, get over it.
To dream that you are riding in a horse drawn carriage symbolizes you desire for elegance. You want to be more dainty and higher class. The definition of high class these days is a bit loose however since not all rich people act the same or have the same culture since they do not all come from old money. Just look at Mark Zuckerberg. Either way, this type of dream means that you need to go the extra mile to make yourself a bit classier. You have a desire to go above and beyond to make yourself come off as a bit more of a gentleman or noblewoman.
Not having those stereotypes in society today it is hard to know how to model yourself, but as long as you hold yourself to higher standards in just about everything you have been doing, you will begin to see what it is like to be a bit more classy in these modern times. To dream that some of your friends are in a carriage and you are not suggests that you do not feel as if you meet the standards of the social group that you have put yourself into. You do not think that you have reached a comfortable position in your group of compatriots which is probably leading to feelings of inadequacy. The best way to get past this is to realize how silly it is to hold yourself up to the standards of another or to hold yourself up to standards that you are projecting from someone else's point of view. This is the definition of madness.
The best part about a carriage is that it can carry you from one place to another without you having to put in any effort into it. This could be a great sign for your future that soon you'll be able to glide along a little in life without having to push yourself too hard. This is your reward for all of your hard work, so look forward to it!