For me, I can only really talk about oil paintings and how studying works from all over time has made me feel. I look for more than a pretty painting.
Art is more than aesthetic, it's more to me than just a beauty. A composition that makes you feel relaxed and has all the components and "notes" (brush strokes creating shapes throughout), to create that feeling, is wonderful. A painting that has all the beauty but none of the components of a feeling, is usually lost on me. Some paintings have all of the beauty, but none of that feeling.
There are intentional "feelings" that are brought to a painting, some are forced, some are subtle. I hear rhythm in some, harmony is an accurate word, to feel the stress of a painting vibrate. It seems to me that often a feeling is brought to a painting forcefully, many times I see this when words are added. Reading a painting to me is forced, and lacks imagination, provides few options for interpretation for others, and means the artist either had an extremely complex topic that has depth that reaches further than the words can detail, or it's a lazy way to express a feeling. I use the concept of "words in a painting" as an example, there are many other methods used to invoke a reaction in a forced way. To master the techniques that bring forward these emotions would be a life well spent.
Then there are unintentional "feelings" that an artist brings to a painting. When the artist just feels a certain way and this comes out in the painting. Of course all artists, all people, feel a certain way all the time, and it fluctuates from moment to moment. It's not unusual for a song to bring us joy and sadness and excitement in the same two minute song. When an artist paints there is a feeling, and there is no doubt that every artist, even those young two and four year old artists among us show how they feel when they paint.
Paying close attention to how a child, or otherwise non-artist, goes about their art is insightful to the inquisitive. Are the eyes big, or the forehead, is the ground darker or lighter, is the sun in the picture, where is the light, what colors are used? The questions go on and on, and often the little artist in us all will do the same sorts of things in each of our works, showing a general feeling inside the artist.
I look at works from artists that are hundreds of years old, and I see the same timid marks in some areas, and bold expressions of confidence in other areas. I see complex emotions reveal themselves in a harmony that is hard to comprehend, but there it is. When any artist puts anything down, they reveal, without filter, and often unaware, what deep complex emotions are within. I say, don't force it, let it come out, it reveals itself in an honest way.