The previous answer already got accepted, but I am answering this question just to make sure that things are clear. I will go one step deeper which can be helpful to advanced people.
First of all, cross validation is a model selection mechanism that is used mainly to select hyperparameters. Changing hyperparameters will affect the number of parameters in the model. For example, increasing the number of layers in a neural network can introduce thousands more parameters ( depending on the width of the layer).
Second, almost any training algorithm can have unlimited number of possible hyperparameters. To make sure this is clear, let me give an example: in CNN, the number of layers is a hyperparameter that can take in theory any value between 1 and infinite, which means by just changing this hyparameter, I can generate infinite number of models. At the same time, the number of levels (depth) in decision tree is a hyperparameter that can take also a value between 1 and infinite, which means I can generate infinite number of models using decision tree, yet we use cross validation with decision tree but not cnn!!!!
Do not confused hyperparameters with parameters, cross validation has nothing to do with parameters it is only about hyperparameters and different training algorithms. Changing the values of the parameters will be taken care of by training algorithm.
Let us go back to the original question, why do not we use cross validation with CNN??
In fact, the answer to this question is based on a very important concept in machine learning. Variance error vs. Biased error. Let us say you have N models that you trained, they all have variance error and zero biased error, in this case using cross validation to select a model is not useful, but averaging the models is useful. If you have N models that all have different biased errors (non zero), then using cross validation is useful to select the best model, but averaging is harmful.
Any time you have models that have different biased errors, use cross validation to determine the best model. Anytime you have models that have variance errors, use averaging to determine the final outcome.
CNN has tendency toward overfitting not underfitting. Today we know that the deeper the network the better, but overfitting is what scares us.
CNN are good targets for averaging rather than selection, that is why some times they train four or five models and then they average their outputs.
The concepts to select network architecture, was studied in literature. They made it clear how to select your hyper parameters. In fact, if you have a lot of data just go for larger models.
I recommend you read the following papers:
1- Alex- Hinton paper in 2012, the paper where Alex proposed his network. You will see that most of the tricks they proposed is to deal with overfitting (variance error) and not biased errors.
2- super learner,
Super Learner In Prediction
This paper explains mathematically what is cross validation. Many people think about cross validation as a set of training/testing experiments that scans a set of parameters and returns the best model, but they ignore if this is enough to guarantee that this is the best model I can get using the training data available. They also ignore all the assumptions that cross validation needs to guarantee that the returned model is the super learner.