Not being able to see your document, cannot answer specifically. However, if you received a document, then it probably will affect you, otherwise, they would not have sent it.
For a horizontal well, frequently the surface location may not be in the section(s) where they intend to perforate. The well is drilled fairly vertically down to the reservoir and then they make the turn to horizontal. That turn can take 1/4th mile, so they do not want to waste it in the sections of interest. Hopefully, there will be a map of the intended pathway of the well in the documents and you will be able to see where it will cross your acreage. Timing may be an issue. In some states, the permits have a short time frame and they have to drill or the permit expires. Not sure about WY. I have heard that their permits can have a very long time frame. Read the documents carefully as they will tell you what you need to know.
The surface owner needs to have a surface use agreement with the drilling operator. That can be separate from the mineral lease if the surface owner is different than the mineral owners.
The bottom hole of that well if drilled will be in Sec. 35 T39N, R66W. So the SW corner of that drilling unit, touches the NE corner of your section, but the well will not extract from your section. The exact well plan has not yet been uploaded to the WOGCC web site yet though. You could check there later. I think there is a rule in WY about notifying adjacent owners which may be why you were notified. However, you could give them a call & ask. Permits in WY are good for 2 years from the date they are submitted not from the date they are approved. Because of the large number of permits, the state asks the companies to submit their 6mo or 1 yr drilling plan & then they approve them only a month or 2 before planning start date (SPUD date).
http://pipeline.wyo.gov/wyodall.cfm?nAPINO=2727423&nApi=2727423&Oops=1