Horsey took the early lead, after four birdies in a row from the seventh to ensure he was right in the mix alongside Wall, who carded a bogey-free opening round.
Another Englishman Tyrrell Hatton carded 30 on the front-nine, including an eagle on the par five third, to finish his round two shots off the lead in fourth spot.
Four-time major winner Rory McIlroy, twice a winner in Dubai, finished in a five-strong group at seven-under alongside Dane Lasse Jensen, England's Chris Paisley, Alexander Bjork of Sweden and Belgium's Thomas Pieters.
McIlroy, who returned from a three-month absence owing to a rib injury to finish joint-third in Abu Dhabi last week, hit a bogey-free round to remain in contention.
"I didn't expect to play as well as I did last week and it's been nice to continue that into this week," McIlroy said.
"The greens in the morning are perfect and there wasn't much wind for probably the first 12 or 13 holes. So you needed to take advantage of it today. Thankfully I was able to do that."
Spaniard Miguel Angel Jimenez, South African duo Darren Fichardt and Haydn Porteous, Irishman Paul Dunne and China's Li Haotong were six under, a shot clear of a group containing defending champion Sergio Garcia.
Englishman Danny Willett endured a difficult opening day as he dropped three shots on the eighth and another four on the ninth to finish five-over at the bottom of the leaderboard.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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