When I was doing enthalpy, this was one of the tricky concepts that I still sometimes get wrong. Here is how you are supposed to remember it.
- Identify the System
- The system is where the reaction happens. You cannot physically monitor the change in heat here. The change you always measure happens in the surroundings.
- Identify the Surroundings
- This is the surroundings where usually the change is expressed as.
Now that we got the basics cleared away, let us look at your problem.
My reasoning: if the temperature of the solution decreases, it means
heat was released into the surroundings, so the enthalpy change is
This is what I usually think of, but now you must understand that as I've said before the change always happens in the surroundings and is associated with the surroundings. So the temperature of the solution decreases, which means that the surroundings temperature decreased. The solution is part of the surroundings. This means that the temperature of the system increases. Thus making the $\Delta H$ positive and the reaction endothermic.
Good Question, always remember that you cannot, in most situations, physically measure the change in the system.