Did Ellen White say anything about dinosaurs?

Ellen White did not mention dinosaurs by name. Many people, though, think she was referring to them in statements such as the following, from the Spiritual Gifts volumes. If this is correct, the first one answers your question about whether they were on the ark:

Every species of animal which God had created were preserved in the ark. The confused species which God did not create, which were the result of amalgamation, were destroyed by the flood (Spiritual Gifts, 3:75).

Bones of men and animals are found in the earth, in mountains and in valleys, showing that much larger men and beasts once lived upon the earth. I was shown that very large, powerful animals existed before the flood which do not now exist. Instruments of warfare are sometimes found; also petrified wood. Because the bones of human beings and of animals found in the earth, are much larger than those of men and animals now living, or that have existed for many generations past, some conclude that the world is older than we have any scriptural record of, and was populated long before the record of creation, by a race of beings vastly superior in size to men now upon the earth (Spiritual Gifts, 3:92, 93).

There were a class of very large animals which perished at the flood. God knew that the strength of man would decrease, and these mammoth animals could not be controlled by feeble man (Spiritual Gifts, 4a:121).

The first statement indicates that the “confused species which God did not create” were the result of “amalgamation,” and they were not preserved in the ark but perished in the Flood. Mrs. White did not spell out how this amalgamation came about. Attempts to define it more precisely are of necessity just speculation. I do not know whether or not human beings had a part in that. Mrs. White simply does not say.

See also the following question and answer.