Embroidery Clothing Logo for Family Lodge

This is what Trail's End Lodge - Est. 1969 was looking for in their logo design

We are looking for a logo design for our family hunting lodge that has been in the family since 1969. It is a remote camp located deep in the Canadian woods on the banks of a small river. There is primarily maple, oak, white birch and pine trees on the property. The main wildlife is white tail deer, moose and black bear.
The logo will be embroidered on clothing such as hats, shirts and more for family and friends.
Attached image is a rough example of a concept that we like.
Feel free to tweak this example or provide a different concept.
A rustic look is preferred.
Approximately 3" wide by 2" tall.
Image of a antlered white tail deer is preferred... note that in my example, the white box and boarder around the deer is not required. Read more