I@Tara506
YOu can certainly increase your minimum rate - but I'm gathering what you want as "minimum" for the high season is a lot higher than your "minimum" for the low season?
If you have multicalendar ( ie you have more than one listing) You could use "rule sets" to apply to higher seasons which sounds like exactly what you are after. A sneak option - you could duplicate your listing, then snooze it - airbnb would still recognise you have more than one listing and you could use the rule set option. bit of mucking around in the first instance but a good long term solution.
OR you could duplicate your listing have one minimum price for high season for the 2nd version and another lower minimum for the original version - just block out dates on the original one for high season so that it can't be booked at a low price. Teh draw back with this plan is that your new second duplicate version will have no reviews. I think the multi calendar idea is the best option. Other more experienced hosts may have other ideas...