The question as to whether angels have wings has been kicked around by Christians since the earliest days. The Bible is rich with symbolism and the wings of angels is one of them. Joseph said, “An angel of God never has wings.” This single quote has ended the discussion among most LDS members when the topic is mentioned. The quote is not scripture, but was taken from Wilford Woodruff’s journal. (see Journal of Wilford Woodruff, vol. 2, 27 June 1839, Historical Department, The Church of Jesus Christ of Latter-day Saints, Salt Lake City).
I would say that the vast majority of angels that appear to us will NOT have wings. They are messengers sent from God, and there are many types, but that doesn’t mean they cannot have wings. Journal entries are not always the best sources. I will tell you that I know that there are angels and holy creatures that have wings. I also believe that we can use light to create many forms of protection and glory, including wings or winglike forms. In the realm of the Kingdom anything is possible.
There is much unbelief in the Church. Perhaps this is one item worth reconsidering. Why? Heaven is a lot more diverse than you think. Don’t take my word for it, get some revelation for yourself.