In the novel, I could not get a clear idea of just how large Kerowyn's company finally was, when they started the march into Valdemar. Just talking actual soldiers, not support personnel.
2 Answers
Lerryn's "company" was oversized and Kerowyn's was twice as large
Chapter 12 gives a good idea of the size of Lerryn's Skybolts. When the company flees the Karsite forces:
At sunset Lerryn had split the force, taking half of them with him, leaving half with his second in command. Shallan and Relli had gone off with the Captain; Kero had stayed with Icolan Ar Perdin, the second, a dour little man who had survived more routs than Kero cared to think about.
...
Finally the word went around the circle; "There's a fork in the game trail. We're splitting again"
...
They split twice more during the grueling, half-blind trek through the darkness, and when dawn trickled pale pink light over the hilltops and through the thick trees, there were no more than twenty riders left in Kero's group. She didn't know any of them terribly well, except for the leader, the head of all the scout groups, a colourless woman known only as Lyr.
So, after splitting four times, in half once and presumably roughly in half each other time, there are "no more than twenty" in a group. A reasonable assumption is that the original size of the company was somewhere between (16x20)=320 and (16x15=240).
In Chapter 17 we learn that:
...And from the beaten force that had come up from Seejay, tails between their legs, she had built the foundations for a specialist-Company that now tallied twice the number that Lerryn had commanded.
And in many ways it was four companies, not one, each with its own pair of Lieutenants... The largest group was the light cavalry, next came the horse archers. Those two groups made up two-thirds of their forces.
Subsequently the horse archers lost a quarter of their number in the deciding battle of the conflict with Karse. These losses were probably replaced with recruits who were already in training back in the Skybolts' winter quarters at Bolthaven when the company returned prior to the midwinter march to Valdemar, especially as there was the remainder of winter to complete their training before the campaign against Ancar began in spring.
In summary, I would estimate the Skybolts as numbering 500-600 personnel, almost all of whom were combatants. This is a battalion-equivalent force, but given that "in many ways it was four companies" this makes sense. Clearly "Company" is a term for a mercenary organisation, rather than designating a specific number of troops, at least where the Skybolts are concerned.
The Skybolts are repeatedly described as a military company.
A company is a military unit, typically consisting of 80–250 soldiers and usually commanded by a major or a captain
This description is backed up toward the end of the novel.
Heralds don’t have to command a few hundred hot-blooded, hard-headed fighters, each of whom is at some time or other convinced he could Captain the Company better than you.
Note that the Skybolts are continually recruiting which means that their numbers fluctuate throughout the novel, probably from a high of about 300 down to around 150 later in the book, based on the fact that at one point approximately half of their number are killed (and the company seriously considers retreating back to their training ground to reinforce).
By the time they head back to Valdemar they're not up to full strength again, but they do have sufficient resources for a bunch of mages, healers and three horses per mounted fighter, plus various hangers-on. This gives us a rough force strength of about 200 men, 400 horse and probably another 25 camp followers of varying descriptions at the point in the book you've mentioned.