Small Greenhouse Thermal Losses:

All small greenhouses suffer from the geometric reality of a high surface area to volume ratio.  To understand this a simple geometric sequence is useful.  The sequence is analyzing ever larger cubes and the ratio of their exterior surface area to the enclosed volume.  For example:

1-ft x 1-ft x 1-ft =   6-ft2 surface area;     1-ft3 volume  =  6   ratio of surface area / volume
2-ft x 2-ft x 2-ft = 24-ft2 surface area;     8-ft3 volume  =  3   ratio of surface area / volume
3-ft x 3-ft x 3-ft = 54-ft2 surface area;   27-ft3 volume  =  2   ratio of surface area / volume
4-ft x 4-ft x 4-ft = 96-ft2 surface area;   64-ft3 volume  =  1.5 ratio of surface area / volume

Further, regardless of greenhouse size, construction materials are typically the same.  Hence the insulating value of an exterior square foot of a “standard” greenhouse of any size is equal. This leads to the unavoidable conclusion:  
The smaller the greenhouse, the quicker it losses heat.  The only way to combat this is through better insulation and reducing air leakage.
These are examples of a small 8-ft x 16-ft greenhouse size using various levels of construction to show the impact of improvements in insulation and air-leakage have on heating load on cold nights. The last column is a 15-ft diameter cold-climate geodesic dome greenhouse as another common option. The ACH (air changes per hour) factor covers the fact the greenhouses are not fully air-tight.  High-tunnel plastic sheet covered greenhouses tend to leak more air (hence ACH 2).  It is possible that the other two greenhouse models leak less than 1-ACH, but using this value is not unreasonable.

GH heat-loss comparison

                                                                 High-tunnel             Quality poly-glazed                 15-ft  dia. Dome
Glazing                                              6-mil plastic sheet  8mm twin-wall polycarbonate 16mm 5X-wall polycarbonate
ACH (air change per hour)                         2                                 1                                                 1
Glazing R-value:                                        0.9                                1.7                                               2.7*
Heat loss: Btu/hr-F                                  667                             352                                               155
Interior temperature F  steady-state   15 + 8 = 23F               15 + 15 = 30F                               15 + 33 = 48F
Final row: temperature inside greenhouse on 15F night using 1500W heater running continuously.
*condensation on glazing overnight reduces R-value (2.3 for dome yields lower in-dome over night temperature of 44F).
The above table clearly shows why trying to keep a standard (fully-glazed) greenhouse heated in cold weather is impractical and electrically expensive (if electric resistance heat is used).  The dome is much better for two reasons: 1) lowest surface area to volume ratio and 2) better glazing.

I have designed a 8.4' x 16.4' 138-sqft greenhouse with a heat-loss-rate of just 102 Btu/hr-F (using the same ACH = 1).  On a 15F night the 1500W heater will warm the greenhouse interior to 65F.  Full design DIY plan are in the works. from: TerraPoniK greenhouses, "Engineered for Growth"

The heat loss in our 8x10ft is a thing, but mitigated with soil colour, moisture, and mulch.  Storing the heat in the soil helps reduce nighttime lows.

the biggest problem we find is air flow in the heat of the day and generally overheating.  It easily gets 120f on 80f days.  Well, probably much hotter, but the min max thermometer only goes to 120f.  At night it might get down to 70f if it's cool here.  Tomatoes stop setting when they get too hot.  

These are temperature with the door and window open.  It's a mid (20th) century glass and aluminum greenhouse

Bigger greenhouse setups we've tried seem to stay more even in temperature.  The larger amount of earth helps hold the heat.  We can also fit large rain barrels for thermal mass.  

As a rare type of human whose surface area to volume is much crappier than average, the OP's math has much validity. Years ago, I read a well-respected book about green houses whose author stated emphatically that any greenhouse smaller than 10 ft by 12 ft would struggle for all the reasons stated by both Kevin and r ransom.

More recently, I read another well-respected book and did a review here: https://permies.com/wiki/143395/Chinese-Greenhouse-Dan-Chiras#1213651
Much of what Dan Chiras said made huge amounts of sense to me. Yes, in our cloudy winters, we may benefit from more glazing than some greenhouses that only glaze part of the roof and the southern exposure, but glazing a north wall is just asking for more difficulty managing temperatures than is necessary, and doesn't add enough light in the winter to balance the heat loss.

I have much respect for a few of our local farmers who shut down their greenhouses from November to the end of January to avoid our shortest, cloudiest days, rather than throwing good energy after bad. They're working with what the industry standard was when energy was cheap. It is possible to build more intelligent greenhouses. There are good examples out there. I suspect it is difficult to change what's been done by so many farmers for the last 40-60 years.