@Dan DeGroff - I appreciate the reply and additional details. From a lending perspective, the home in Colorado should be purchased and occupied as a 2nd home (yes, even if you're a first-time home buyer and don't own a primary residence currently). The scenario as a 2nd home will make the most amount of sense to an underwriter (traveling to a different location for work and the property is located in a resort-type area). The truth is, you don't have the intent to occupy this home year-round as a primary residence, but you do have the intent to occupy it for a portion of the year (during ski season).
A primary residence is a place you plan to live for pretty much year-round. A primary residence is not intended to be a rental property. Even Robert Kiyosaki calls a primary residence a liability, but we all need a place to hang our hat, right? If you're getting a roommate to help cover the costs of bills and expenses, that's one thing, but you would need to be living there.
House hacking: you would actually occupy the home for a minimum of the first 12 months. You can get roommates during this time, but YOU need to live there too. After 12 months, you've met the occupancy requirement on your deed of trust, and you can convert the property to a rental property after that.
There's nothing in the Fannie Mae/Freddie Mac guidelines that says you can't rent out a 2nd home when you're not occupying it, and you could rent it out as a short-term rental or long-term rental when not in use (double check the local laws regarding short-term rentals). You can not rely on rental income to help you qualify on a 2nd home transaction, and you can put as little as 10% down on a 2nd home.
As for the 2nd part of your question: "Cash offer on distressed home in the Winter, rehab etc" - if you're paying cash, there isn't a loan, so you don't need to declare/specify occupancy when paying cash. On the refinance (take-out loan) you would need to declare occupancy, and I'm guessing the plan is to fully rent the property at that time (e.g. BRRRR), so you would run the cash-out refinance as an investment property/occupancy on that loan. $100K is enough to get you started. I've done multiple deals for that amount or less, and I actively have clients working in that range right now too.
In short, you get one primary residence. If you decide to house hack, you must live there for the first 12 months. You can have roommates while you're living there, but you can't occupy the home for only 5 - 7 months, move out, and completely rent it out. After 12 months, you can fully rent out the property if you desire, without needing to occupy.
2nd homes are designed to have another place to live in a "resort type" area or when commuting to a different state for work. You can rent these out (STR or LTR) when not in use, but you can not use rental income to help you qualify for the loan.
Investment properties = you have no intention of ever occupying the home. You can use rental income to help you qualify for the loan.
Additional Resources:
Occupancy Types | Fannie Mae
Occupancy Fraud May Be the Next Risk for the Mortgage Industry | CoreLogic®
Feel free to reach out if you have any additional questions.