There seem to be two companies by this name. One is Aldon Accessories Ltd. Japan, which seems to be the vintage and original, and the other is Aldon Accessories Ltd. (C) 1986 NYC. The US Aldon's appears to make musical carousel figurines made of porcelain, the same as Japan had, but they make their's in Taiwan. .
Apparently they sued Spiegel in 1982 for copyright infringement and it was because of the Unicorn and Pegasus. They won the suit.
But it also seems they have moved all over the world. They started in Japan, then went to New York. The only way I can tell the dates is by the date on the horse or music box. They kept making them in Japan for awhile it appears, but there are some made in Taiwan. And I cannot find anything except Music boxes and Unicorns. They have lots of other animals that are quite common. However, I don't find any recent dates and I don't know if the company still exists.
Shown above, left: Standing Horse in Black
Shown as "Speak Softly," Missouri Fox Trotter stallion owned by Karen Grimm
Porcelain Music box Pegasus, Japan
Vintage 1980. From eBay auction; used by permission.
Rearing Unicorn Japan Aldon
This is a chalky "grained porcelain" Unicorn made in Japan. No date on this one. Used by permission.
Rearing Unicorn NYC Aldon
Made in Taiwan. Dated 1980. Used by permission.
1974 NYC Aldon base/label
Unknown item. Made in Japan. Dated 1978. Used by permission.