I find myself agreeing with both sides of this.
OP - You have the right, as a paying customer, to be upset that the business you contracted with did not hold up their end of the agreement.
They did not make you feel like a valued customer or any kind of priority, which is what good customer service should do.
You are also not to blame for ordering from what they had available. Winter or no winter, customers trust that businesses wouldn't offer what they can't provide.
On the other hand, the business was in a "damned if we do, damned if we don't" scenario. Sometimes shit happens.
Here's what I would do, if I were the customer, having been raised by former restaurant owners with guidance on how to complain.
I'd call them up and politely, calmly ask them to make my spring chick order free. 
Yes, the refund and the free chicks.
Because this has been an inconvenience, because I feel devalued being thrown to the end of the line, because I haven't submitted a review for my experience yet.
When the first person says "No" in the blah-blah policy-speak, you just patiently, kindly, explain it all again.
1. What happened. 2. How that's affected you. 3. What resolution would satisfy you.
Yes, I would like to speak to your manager, please. Rinse, Lather, Repeat. Stay nice.
The thing is, any half-decent customer service is obligated to stay on the line with you until you acquiesce, they're not allowed to hang up. So, you just have to wait them out, and let them work through their policy arsenal. Don't take any of it personally. Keep in mind the representative is not to blame.
My parents taught me, from a business standpoint, it's important to get solid feedback form customers, and to learn what's a hard line in the sand that customers won't let them cross. Because a business is profit hungry, it's easy to lose touch with the people who keep it afloat.
Without the opportunity to improve, a bad reputation spreads and the customer base dwindles. It's not just about you, it's every customer that encounters the same scenario with them. Should their current approach be set in stone, or can they learn to be more accommodating?
That's why I always complain when I'm disappointed by a business. If they make it right, I get the chance to sing their praises.
And yes, I've worked in customer service myself, and yes I've dealt with difficult customers. I have to say I felt better when I could fix something than when a customer walked away unhappy. I would rather they give me the chance to make it right.
They can't give you the ship date you want but they could comp your next order. However, this does have a better chance of success if you haven't disparaged them first.