Iceland is such a fantastic country to explore - the range of weather, terrain and vistas that you’ll encounter is amazing. Make sure you’ve got a good, reliable vehicle, know the weather forecasts and also have a backup plan when the weather forecast inevitably changes at the last minute.
Regardless of when you go, you’ll need warm clothes and something to block the fierce wind, rain, sleet and snow. I haven’t been in the height of summer but from what i’ve heard it’s still not ever really “warm”. I’ve visited in both March and April and both had every type of weather possible - we didn’t get really heavy snow in April but it’s no unheard of for that time of year. When we visited in March we definitely needed thermal underwear and heavy jackets to anywhere close to comfortable.