Right now it has a floor
RAW is undefined, because dome is undefined
Dome and hemisphere are not defined in the spellcasting section (PHB p201), unlike cone and sphere. A hemisphere might be something very clear for a mathematician, but the game was designed by laymen for laymen. No mathematician would agree with the game's definition of line either.
Until an errata comes out on this, no one really knows if a hemisphere is supposed to have a floor or not, not even the game developers:
The latest tweet says it has a floor, but its arguments are as (un)convincing as the previous one's.
So right now it has a floor
Play the way it makes sense, independent from any tweets
A new one might come out in the middle of your next gaming session anyway.
The intent of the spell is indeed to keep the enemies out, and the majority of the monsters, if not straight out possessing a burrowing speed or phasing ability, is smart enough to dig. IRL dogs have dug under fences to get to the chickens, and they have an Intelligence of 3 in the game. This is setting the bar pretty low.
If it is that easy to get in, you still have to keep a sentry inside. Not what you expect from a 3rd level spell, I would not even take it in a 1st level slot.
Another consideration is the sentence about the weather:
The atmosphere inside the space is comfortable and dry, regardless of the weather outside
If you set it up in a muddy field, during rain, how could it be dry without a floor?
If you are in the mountains, or on a hillside, not having a floor leads to hilariously silly results. Sometimes it is not possible to find even ground for hours.
Carrying around a shovel is not only embarrassing for a powerful wizard, but digging in hard rock or frozen ground is close to impossible.
Leomund is a renowned archmage, why would he create a protective spell that does not really protect?
History of the game
In previous editions, it always had a floor (SRD)
RAW is flexible, now it has a bottom.
But it may change soon again, so I suggest to keep playing the only way it makes sense; with a bottom.
Otherwise Leomund's Tiny Hut is a silly, seriously underpowered spell, which is next to useless except in ideal, rare conditions.