(For this, I'm going to forget that the dragons with no abilities would probably have died out or be a lower-developed race by their middle-ages. Maybe they developed to be stronger or more intelligent, so survived alongside the dragons with abilities. But anyway, here are some thoughts...)
I think if these dragons are sentient, at our level, say, then they would have the capacity to build on what they already have. I think they would develop a lot of fire-based tech and ice-based tech. Like a helmet that concentrates and extends the throw of their breath, or maybe a hand-held extended fire thrower and intensifier, also fuelled by their breath. They would have naturally learned in the past what makes, for example, the fire dragon's fire hotter, more destructive, more intense, as well as what would weaken the effect. They would incorporate this knowledge into weapon and armour designs.
One of the first things developed would probably be armour to protect against these 'special' abilities. This may be full or partial (light) body armour, or possibly a shield that deflects another dragon's breath. A standard dragon shield, for example, would be in two parts separated as much as possible, so the freezing/heating of the front part was not transferred to the inner part of the shield, held by the defending dragon.
The different species would prefer different fighting styles. The ice and fire dragons would rely, pretty much solely, on extending that ability for close to medium range combat, so would need to fly pretty close to be effective. The species without these abilities would prefer to stay well back. Evasion, covert and long-rage attacks would be what they concentrate their development on. Large arrow-firing machines could be held up by multiple dragons or hid in the terrain below. Smaller crossbows or something similar could be attached to or held by, a dragon. They might have developed fire-arrows or explosive arrows. They may have claw-like battle-axes or swords as a last resort, especially if the special abilities can run out at some point.
Another attack method would be similar to birds of prey. They would swoop covertly from above to grab, grapple and pierce their prey with their claws or simple stabbing tools. This would be a get in, get out, repeat type attack used in combination with other attacks from other fronts.
These would all be medieval-type tech.