I did some further digging and indeed the 150,000 number is the amount of stallion during Xuan De, however, The Yong Le era still doesn't have that much more stallions.
The whole Ming empire has 4 major horse breeding industry, they are in Shang Xi, Gang Su, Liao Dong and Bei Jing.
Here is a graph of the horses within the different Ming prefectures, The first is Yong Le(1403~1424) the second is Wang Li(1573~1620)
明代各镇马额数表[24] 单位:匹
镇名|永乐(1403~1424年)年间原额|万历(1573~1620年)初年现额
蓟镇:蓟州|10,700| 6,399
蓟镇:密云| 2,032| 13,120
蓟镇:永平| 6,083| 15,080
蓟镇:昌平| 3,015| 5,625
辽东|77,001| 41,830
保定| 1,199| 4,791
宣府|55,274| 33,147
大同|51,654| 35,870
山西| 6,551| 24,764
延绥|45,940| 32,133
宁夏|22,182| 14,657
固原|32,254| 33,842
甘肃|29,318| 21,660
The source is from (明)《万历会典》卷129~131《镇戍》4~6《各镇分例》1~3(参阅吴晗:《读史劄记·明代的军兵》第94~105页)。
Thus during Yong Le times, there is 343,202 stallions. And 282,918 stallions during Wang Li.
Interestingly, the northwest has the biggest portion of the industry with
129,694 stallions or 38% of the entire empire during Yong Le while 102,292 stallions, or 36% during the period of Wang Li.
So in conclusion, at their height, the Qin has 50,000 stallions, Han has 450,000 stallions, the Tang has 706,000 stallions, the Ming has 343,200 stallions, and the Qing has 226,500 stallions.
However the Ming horse quality is not as good as the other dynasties(except maybe Qin) whil the Qing era is much less cavalry based than the others so horse is not an accurate measurement of its military strength.