I want to know if any of the pictures from my trail camera include deer. It sounds like Rekognition might be the answer for this.
I would go with a DIY solution, since Rekognition will get expensive quick ($1/1000 images). If you did 1fps running continuously, you'd pay $87/day.
Nearly any ML framework with an ImageNet pre-trained model will work. Accuracy will be better if augmented with more labeled deer images (ImageNet probably only has frontal poses) but should be alright straight out of the box.
You could run the whole thing locally on a cheap android phone for free instead of AWS cloud pricing, 1fps will be fine with TensorFlow or MXNet on Android. Then just setup email alerts.