Yes, it seems from scripture, some animals will be in heaven.
Animals must have a soul, but unlike humans they do not have a spirit.
Which animals? - we are given some details in the scriptures.
How many? - we do not know?
Will they be the pets of humans, or believers? - again we don't know, scripture is not that specific on this topic.
Isaiah 11:6-9 (NKJV)
6 "The wolf also shall dwell with the lamb, The leopard shall lie down with the young goat, The calf and the young lion and the fatling together; And a little child shall lead them.
7 The cow and the bear shall graze; Their young ones shall lie down together; And the lion shall eat straw like the ox.
8 The nursing child shall play by the cobra's hole, And the weaned child shall put his hand in the viper's den.
9 They shall not hurt nor destroy in all My holy mountain, For the earth shall be full of the knowledge of the LORD As the waters cover the sea.
Isaiah 65:25 (NKJV)
25 The wolf and the lamb shall feed together, The lion shall eat straw like the ox, And dust shall be the serpent's food. They shall not hurt nor destroy in all My holy mountain," Says the LORD.
There are references to horses in heaven Revelation, but these are symbolic. But there is also this verse although it could be referring to heavenly creatures there are now.
Revelation 5:13 (NKJV)
13 And every creature which is in heaven and on the earth and under the earth and such as are in the sea, and all that are in them, I heard saying: "Blessing and honor and glory and power Be to Him who sits on the throne, And to the Lamb, forever and ever!"