There's a lot that goes into that with the combination of humidity, temp and pressure. Even though it may be summer time, you will still have temperatures at which you can have those ice crystals. In fact, you can have a higher chance of getting into icing in the summer. For example, I was making a quick hop from Bogota, Columbia to Panama City, Panama. I was cruising at FL280 at night and suddenly got into some severe icing. It started with heavy precip that we could hear pelting the windscreen and fuselage. Then came the TAT fail warnings along with air data and TAS warning. The auto throttles kicked off all when it happened. The icing was so bad that the TAT heaters could not keep up with it. After a minute or so, we exited the clouds and all of the warnings went away. We turned the auto throttles back on and went on our way. The standard day temp at FL280 is -40C. At -40, it's generally too cold for icing.
What happens in the summer time, especially near the equator, you get those major storms with frontal passages. These big storms will throw up a lot of moisture and warm air high into the atmosphere. We call them hot towers. As you get close to these storms, the warm air and moisture is perfect for severe icing. There have been many reports of aircraft losing engine power because those ice crystals start to choke off the the engine near the first stage of compression and cause the engines to roll back to a lower setting until you exit conditions.
In all, the conditions will determine where you will see the crystals/ice halos. It's just like contrails. Flying in the AOR, they would put the contrail altitude in your paperwork. That way, you can ensure to stay below it so you are harder to find visually. That altitude changes depending on conditions.
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